Ep pp ts

6/18/2014

1

OPTICAL FIBER

1

Basic principle Total Internal Reflection in Fiber

2

An optical fiber (or fibre) is a glass or plastic fiber that

carries light along its length.

Light is kept in the "core" of the optical fiber by total

internal reflection.

What Makes The Light Stay in Fiber• Refraction

– The light waves spread out along its beam.

– Speed of light depend on the material used called refractive index.

– Speed of light in the material = speed of light in the free space/refractive index

– Lower refractive index higher speed

3

The Light is RefractedLower Refractive index Region

4

This end travels

further than the

other hand

Higher Refractive index Region

Refraction• When a light ray encounters a boundary separating two

different media, part of the ray is reflected back into the first medium and the remainder is bent (or refracted) as it enters the second material. (Light entering an optical fiber bends in towards the center of the fiber – refraction)

5

Refraction

LED or

LASER

Source

Reflection

• Light inside an optical fiber bounces off the cladding - reflection

6

Reflection

LED or

LASER

Source

http://en.wikipedia.org/wiki/Glass

http://en.wikipedia.org/wiki/Plastic

http://en.wikipedia.org/wiki/Light

http://en.wikipedia.org/wiki/Total_internal_reflection





6/18/2014

2

7

Critical Angle

• If light inside an optical fiber strikes the cladding too steeply, the light refracts into the cladding - determined by the critical angle. (There will come a time when, eventually, the angle of refraction reaches 90o and the light is refracted along the boundary between the two materials. The angle of incidence which results in this effect is called the critical angle).

8

Critical Angle

n1Sin X=n2Sin90o

Angle of Incidence

• Also incident angle

• Measured from perpendicular

• Exercise: Mark two more incident angles

9

Incident Angles

Angle of Reflection

• Also reflection angle


• Exercise: Mark the other reflection angle

10

Reflection Angle

ReflectionThus light is perfectly reflected at an interface betweentwo materials of different refractive index if:

– The light is incident on the interface from theside of higher refractive index.

– The angle θ is greater than a specific valuecalled the “critical angle”.

11

Angle of Refraction

• Also refraction angle


• Exercise: Mark the other refraction angle

12

Refraction Angle

6/18/2014

3

Angle Summary

• Three important angles

• The reflection angle always equals the incident angle

13

Refraction Angle

Reflection Angle

Incident Angles

Refractive Index

• n = c/v– c = velocity of light in a vacuum– v = velocity of light in a specific medium

• light bends as it passes from one medium to another with a different index of refraction– air, n is about 1– glass, n is about 1.4

14

Light bends in towards normal -

lower n to higher n

Light bends

away from

normal - higher

n to lower n

Snell’s Law• The amount light is bent by refraction is given by Snell’s

Law:n1sin 1 = n2sin 2

• Light is always refracted into a fiber (although there will be a certain amount of Fresnel reflection)

• Light can either bounce off the cladding (TIR) or refract into the cladding

15

Snell’s Law

16

Normal

Incidence

Angle( 1)

Refraction

Angle( 2)

Lower Refractive index(n2)

Higher Refractive index(n1)Ray of light

Critical Angle Calculation

• The angle of incidence that produces an angle of refraction of 90° is the critical angle– n1sin(qc) = n2sin(90°)– n1sin(qc) = n2

– qc = sin-1(n2 /n1)• Light at incident angles

greater than the criticalangle will reflect backinto the core

17

Critical Angle, c

n1 = Refractive index of the core

n2 = Refractive index of the cladding

OPTICAL FIBER CONSTRUCTION

18

Core – thin glass center of the fiber where light travels.Cladding – outer optical material surrounding the core

Buffer Coating – plastic coating that protect the fiber.

6/18/2014

4

OPTICAL FIBER• The core, and the lower-refractive-index cladding, are

typically made of high-quality silica glass, though they

can both be made of plastic as well.

19

NA & ACCEPTANCE ANGLE DERIVATION

• In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light.”

• optical fiber will only propagate light that enters the fiber within a certain cone, known as the acceptance cone of the fiber. The half-angle of this cone is called the acceptance angle, θmax.

20

21

When a light ray is incident from a medium of refractive

index n to the core of index n1, Snell's law at medium-core

interface gives

• Substituting for sin θr in Snell's law we get:

By squaring both sides

Thus,

22

• from where the formula given above follows.

• NUMERICAL APERATURE IS

• ACCEPTANCE ANGLE

• θmax =

23

Definition:-• Acceptance angle:-

• Acceptance angle is defined as the maximum angle of incidence at the interface of air medium and core medium for which the light ray enters into the core and travels along the interface of core and cladding.

• Acceptance Cone:-

• There is an imaginary cone of acceptance with an angle .The light that enters the fiber at angles within the acceptance cone are guided down the fiber core

• Numerical aperture:-

• Numerical aperture is defined as the light gathering capacity of an optical fiber and it is directly proportional to the acceptance angle.

24

http://en.wikipedia.org/wiki/Refractive_index



http://en.wikipedia.org/wiki/Silicon_dioxide

6/18/2014

5

• Three common type of fiber in terms of the material used:

• Glass core with glass cladding –all glass or silica fiber

• Glass core with plastic cladding –plastic cladded/coated silica (PCS)

• Plastic core with plastic cladding – all plastic or polymer fiber

25

Classification of Optical Fiber Plastic and Silica Fibers

26

BASED ON MODE OF PROPAGATION

• Two main categories of optical fiber used in fiber optic communications are

• multi-mode optical fiber

• single-mode optical fiber.

27

Single-mode fiber

Carries light pulses along single path Multimode fiber

Many pulses of light generated by LED travel at different angles 28

Based on the index profile

29

The boundary between

the core and cladding

may either be abrupt,

in step-index fiber, or

gradual, in graded-

index fiber

Step Index Fibers• A step-index fiber has a central core with a uniform

refractive index. An outside cladding that also has a

uniform refractive index surrounds the core;

• however, the refractive index of the cladding is less than

that of the central core.

The refractive index profile may be defined as

n(r) = n1 r < a (core)n2 r ≥ a (cladding)

30

http://en.wikipedia.org/wiki/Multi-mode_optical_fiber



http://en.wikipedia.org/wiki/Single-mode_optical_fiber



http://en.wikipedia.org/wiki/Step-index_profile



http://en.wikipedia.org/wiki/Graded-index_fiber



6/18/2014

6

GRADED-INDEX • In graded-index fiber, the index of refraction in the

core decreases continuously between the axis and the cladding.

• This causes light rays to bend smoothly as they approach the cladding, rather than reflecting abruptly from the core-cladding boundary.

3132

Figure.2.6

(a)

(b)

• multimode step-index fiber

– the reflective walls of the fiber move the light pulses to the receiver

• multimode graded-index fiber

– acts to refract the light toward the center of the fiber by variations in the density

• single mode fiber

– the light is guided down the center of an extremely narrow core

33

Figure 2.10 Two types of fiber: (Top) step index fiber; (Bottom) Graded index fiber

34

Attenuation

• Definition: a loss of signal strength in a lightwave, electrical or radio signal usually related to the distance the signal must travel.

Attenuation is caused by:

• Absorption

• Scattering

• Radiative loss

35

Losses

• Losses in optical fiber result from attenuation in the material itself and from scattering, which causes some light to strike the cladding at less than the critical angle

• Bending the optical fiber too sharply can also cause losses by causing some of the light to meet the cladding at less than the critical angle

• Losses vary greatly depending upon the type of fiber

– Plastic fiber may have losses of several hundred dB per kilometer

– Graded-index multimode glass fiber has a loss of about 2–4 dB per kilometer

– Single-mode fiber has a loss of 0.4 dB/km or less36

6/18/2014

7

Macrobending Loss:

• The curvature of the bend is much larger than fiberdiameter. Lightwave suffers sever loss due to radiation ofthe evanescent field in the cladding region. As the radius ofthe curvature decreases, the loss increases exponentiallyuntil it reaches at a certain critical radius. For any radius abit smaller than this point, the losses suddenly becomesextremely large. Higher order modes radiate away fasterthan lower order modes.

37

Micro bending Loss

• Micro bending Loss: microscopic bends of the fiber axis that can arise when the fibers are incorporated into cables.The power is dissipated through the micro bended fiber, because of the repetitive coupling of energy between guided modes & the leaky or radiation modes in the fiber.

38

Dispersion

• The phenomenon in an optical fibre whereby light photons arrive at a distant point in different phase than they entered the fibre.

• Dispersion causes receive signal distortion that ultimately limits the bandwidth and usable length of the fiBer cable

The two main causes of dispersion are:

Material (Chromatic) dispersion

Waveguide dispersion

Intermodal delay (in multimode fibres)

39

• Dispersion in fiber optics results from the fact that in multimode propagation, the signal travels faster in some modes than it would in others

• Single-mode fibers are relatively free from dispersion except for intramodal dispersion

• Graded-index fibers reduce dispersion by taking advantage of higher-order modes

• One form of intramodal dispersion is called material dispersion because it depends upon the material of the core

• Another form of dispersion is called waveguide dispersion

• Dispersion increases with the bandwidth of the light source

40

Advantages of Optical Fibre

• Thinner

• Less Expensive

• Higher Carrying Capacity

• Less Signal Degradation& Digital Signals

• Light Signals

• Non-Flammable

• Light Weight

41

Advantages of fiber optics

42

Much Higher Bandwidth (Gbps) - Thousands ofchannels can be multiplexed together over one strandof fiber

Immunity to Noise - Immune to electromagneticinterference (EMI).

Safety - Doesn’t transmit electrical signals, making itsafe in environments like a gas pipeline.

High Security - Impossible to “tap into.”

6/18/2014

8

Advantages of fiber optics

Less Loss - Repeaters can be spaced 75 miles apart(fibers can be made to have only 0.2 dB/km ofattenuation)

Reliability - More resilient than copper in extremeenvironmental conditions.

Size - Lighter and more compact than copper.

Flexibility - Unlike impure, brittle glass, fiber isphysically very flexible.

43

Fiber Optic Advantages• greater capacity (bandwidth up

to 2 Gbps, or more)

• smaller size and lighter weight

• lower attenuation

• immunity to environmental

interference

• highly secure due to tap

difficulty and lack of signal

radiation

44

Disadvantages of fiber optics

• Disadvantages includethe cost of interfacingequipment necessary toconvert electricalsignals to opticalsignals. (opticaltransmitters, receivers)Splicing fiber optic cableis also more difficult.

45

Areas of Application

• Telecommunications

• Local Area Networks

• Cable TV

• CCTV

• Optical Fiber Sensors

46

Formula Summary

• Index of Refraction

Snell’s Law

Critical Angle

Acceptance Angle

Numerical Aperture47

v

cn

2211sinsin nn

1

21sin

n

nc

2

2

2

1

1sin nn

2

2

2

1sin nnNA

STUDENTS YOU CAN ALSO REFER IT……

48

http://hank.uoregon.edu/experiments/Dispersion-in-Optical-Fiber/Unit_1.6%20(2).pdf

http://www1.ceit.es/asignaturas/comuopticas/pdf/chapter4.pdfhttp://course.ee.ust.hk/elec342/notes/Lecture%206_attenu

ation%20and%20dispersion.pdf

1 Engineering Physics by H Aruldhas, PHI India 2 Engineering Physics by B K Pandey , S. Chaturvedi, CengageLearning 3 Resnick, Halliday and Krane, Physics part I and II, 5th

Edition John Wiely4 Engineering Physics by S.CHAND5 Engineering Physics by G VIJIYAKUMARI

http://hank.uoregon.edu/experiments/Dispersion-in-Optical-






http://hank.uoregon.edu/experiments/Dispersion-in-Optical-Fiber/Unit_1.6 (2).pdf

http://www1.ceit.es/asignaturas/comuopticas/pdf/chapter4.pdf

http://www1.ceit.es/asignaturas/comuopticas/pdf/chapter4.pdf

http://course.ee.ust.hk/elec342/notes/Lecture 6_attenuation and dispersion.pdf

http://course.ee.ust.hk/elec342/notes/Lecture 6_attenuation and dispersion.pdf

6/18/2014

1

Dielectrics are the materials having electric dipole moment permanently.

Dipole: A dipole is an entity in which equal positive and negative charges are separated by a small distance..

DIPOLE moment (µEle ):The product of magnitude of either of the charges and separation distance b/w them is called Dipole moment.

µe = q . x coulmb.m

All dielectrics are electrical insulators and they are mainly used to store electrical energy.

Ex: Mica, glass, plastic, water & polar molecules…

Xq -q

Introduction

+

Electric field

Dielectric atom

+

+

+

+

+

+

+

+

_

_

_

_

_

_

_

__

dipole

The relative permittivity(εr) is often known as dielectric const. of medium it can given by,

εr=ε/ε0

Dielectric constant is ratio of permittivity of medium to permittivity of free space.

The value of capacitance of capacitor is given by,

C0=εrε0A/d

By this eqn we can say that high εr increases capacity of capacitor.

Polar and Nonpolarized MoleculesNon-polar Molecules : The Dielectric material in which

there is no permanent dipole existence in absence of an

external field is …..O=O N N Cl-Cl F-F Br-Br I-I

2 – Compounds made of molecules which are symmetrically shaped

carbon tetra fluoride CF4

propaneC3H8

methane CH4

carbon tetra fluoride CCl4,

carbon dioxideO=C=O

Polar Molecules The Dielectric material in which there is

permanent dipole existence even in absence of an

external field is …..

HClhydrogen chloride

carbon monoxideC O

2 – molecules with O, N, or OH at one end – asymmetrical e.g.; CH2Cl2,CH3Cl

waterH2O

unbounded electron pairs bend the molecule

ammonianitrogen trihydrideNH3

alcoholsmethanolCH3OH

6/18/2014

2

Identify each of the following molecules as

1) polar or 2) nonpolarized. Explain.

A. PBr3

B. HBr

C. Br2

D. SiBr4

7

Identify each of the following molecules as

1) polar or 2) nonpolarized. Explain.

A. PBr3 1) pyramidal; dipoles don’t cancel; polar

B. HBr 1) linear; one polar bond (dipole); polar

C. Br2 2) linear; nonpolarized bond; nonpolarized

D. SiBr4 2) tetrahedral; dipoles cancel; no polar

8

As shown in fig. when an electric field is

applied to dielectric material their

negative & positive charges tend to

align in equilibrium position.

They produce electric dipole inside the material.

This phenomenon is known as Polarization.

It can be represented by,

P=polarization

μ= dipole moment

V=Volume

Unit=Cm-2

Now dipole moment depends upon applied electric field.

α polarizability of material.

PV

E

P E

P E

++++++++

--------

E0

----------------------

++ --++ --++ --++ --++ --++ --++ --++ --++ --++ --++ --

+q

-q

-q

+q

-q

+q

++++++++++++++++++++++

E0

In absence of dielectric

In presence of dielectric

0

0

0

0

0

.E ds q

qE A

qE

A

0

0 0

0 0

. '

'

'

E ds q q

q qEA

q qE

A A

6/18/2014

3

V=Ed

So

Now

0 0

d

E Vk

E V

0

0

0 0

0 0 0

'

',

1, ' (1 )

E qE

k kA

q qE

A A

q q qSo

kA A A

then q qk

0

0

So, . '

1(1 )

q

.

E ds q q

q qk

k

k E ds q

This relation true is for parallel plate capacitor

Which is Gauss’s law for dielectrics

The resultant dielectric field is given by,

Where,

E=Electric field

D=Flux Density or

Displacement vector

P=Polarization

0 0

0 0

0

0

'

',

,

, D

p

q qE

A A

qnow P

A

q PE

A

qE P

A

qnow D

A

So E P

Electric susceptibility:

The polarization vector P is proportional to the total electric flux density and direction of electric field.

Therefore the polarization vector can be written

0

0

0

0

( 1)

1

e

e

r

e r

P E

P

E

E

E

Displacement vector,

0

0

0

r 0 0

0

D E P

N ow ,P=

( - ) E P

(or) ( . - ) E P

( 1) . P

W here,( 1)

r

r

E

E

1. Electron polarization

2. Ionic polarization

3. Orientation polarization

4. Space charge polarization

6/18/2014

4

When no external field is applied nucleus of atom is like in fig. (a)

When external field is applied, displacement in opposite direction is observed between nucleus & electrons due to this dipole moment is induced.

This type of polarization is called Electronic polarization.

Ex. Germanium, Silicon, Diamond etc…

19

+

-

+

-

-

Electric Field (a)(b)

Some materials like ionic crystal does not possess permanent dipole moment.

Fig. (a) shows natural arrangement of ionic crystal. When Ele. Field is applied on this type of material displacement of ions is observed.

Due to an external electric field a positive & negative ion displaces in the direction opposite to each other due to which distance between them is reduced & ionic polarization is generated.

Ionic polarization is observed in materials like NaCl, KBr, KCl etc…

Let us consider simple example of NaClcrystal.

As shown in fig. when crystal is placed in an external electric field Na+ ion displaces in one direction & Cl- ion goes in opposite direction.

Some molecules like H2O, HCl having permanent dipole moment p0.

In the absence of a field, individual dipoles are arranged in random way, so net average dipole moment in a unit volume is zero as shown in fig. (b).

A dipole such as HCl placed in a field experiences a torque that tries to rotate it to align p0 with the field E.

In the presence of an applied field, the dipoles try to rotate to align parallel to each other in direction of electric field fig (d).

This type of polarization is Orientation polarization.

This type of polarization occurs only in polar substances like H2O, CH3Cl when they are placed in external field.

A crystal with equal number of mobile positive ions and fixed negative ions.

In the absence of a field, there is no net separation between all the positive charges and all the negative charges.

6/18/2014

5

In the presence of an applied field, the mobile positive ions migrate toward the negative charges and positive charges in the dielectric.

The dielectric therefore exhibits Space charge or interfacial polarization.

.

?

.

.

dW F dr

F

dW qE dr

dW E dp

p pP

lA V

0

0

0

2

0

2

0

( 1) .

. .( 1) .

. .( 1) .

1( 1) E

2

1( 1) E

2

?

r

r

r

r

r

p PV

dW EVdP

P E

dW E V dE

dW E V dE

W V

W

V

U

References:

Engineering physics By Dr. M N Avadhnulu, S Chand publication

Engineering physics by K Rajgopalan

http://web.mit.edu/viz/EM/visualizations/coursenotes/modules/guide05.pdf

6/18/2014

1

Band Theory of Solid

Objectives

• Effective Mass of electron

• Concept of Holes

• Energy Band Structure of Solids:

Conductors, Insulators and Semiconductors

• Semiconductors

Intrinsic and Extrinsic Semiconductors

• Type of diodes

Simple Diode

Zener Diode

Effective Mass of electron

An electron moving in the solid under theinfluence of the crystal potential is subjected to anelectric field.

We expect an external field to accelerate theelectron, increasing E and k and change theelectron’s state.

dt

dx

dx

dVe

dt

dVe

dt

d

eV

and

dk

dgv

1

gvdx

dVe

dt

dk

dk

d

dx

dVek

dt

d

gvdx

dVe

dt

dkgv

eEkdt

d

dt

dk

dk

d

dk

d

dk

d

dt

d

dt

dva

g

11

kdt

d

dk

d

dt

dk

dk

d

2

2

22

211

eE = F

e

1

m

Concept of Holes

Consider a semiconductor with a small number ofelectrons excited from the valence band into theconduction band.

If an electric field is applied,

• the conduction band electrons will participatein the electrical current

• the valence band electrons can “move into”the empty states, and thus can also contributeto the current.

6/18/2014

2

Concept of Holes

If we describe such changes via “movement” of the“empty” states – the picture will be significantlysimplified. This “empty space” is called a Hole.

“Deficiency” of negative charge can be treated as apositive charge.

Holes act as charge carriers in the sense thatelectrons from nearby sites can “move” into thehole.

Holes are usually heavier than electrons since theydepict collective behavior of many electrons.

Electrical current for holes and electrons in the samedirection

• To understand hole motion, one requires anotherview of the holes, which represent them aselectrons with negative effective mass m*.

• For example the movement of the hole think of arow of chairs occupied by people with one chairempty, and to move all people rise all togetherand move in one direction, so the empty spotmoves in the same direction

Energy Band Structure of SolidsConductor, Semiconductor and Insulator

In isolated atoms the electrons are arranged inenergy levels.

Energy Band in Solid

The following are the important energyband in solids:

Valence band

Conduction band

Forbidden energy gap or Forbidden band

Valance band

The band of energy occupied by the valance

electrons is called valence band. The electrons in the

outermost orbit of an atom are known as valance

electrons. This band may be completely or partial filled.

Electron can be move from one valance band to

the conduction band by the application of external

energy.

6/18/2014

3

Conduction band

The band of energy occupied by the conduction

electrons is called conduction band. This is the

uppermost band and all electrons in the conduction

band are free electrons.

The conduction band is empty for insulator and

partially filled for conductors.

Forbidden Energy Gap or Forbidden band

The gap between the valance band and

conduction band on energy level diagram known as

forbidden band or energy gap.

Electron are never found in the gap. Electrons

may jump from back and forth from the bottom of

valance band to the top of the conduction band. But

they never come to rest in the forbidden band.

According to the classical free electron theory,materials are classified in to three types:

Conductors

Semiconductors

Insulators

Conductors

There is no forbidden gap and the conduction bandand valence band are overlapping each other between andhence electrons are free to move about. Examples are Ag,Cu, Fe, Al, Pb ….

Conductor are highly electrical conductivity.

So, in general electrical resistivity of conductor is very lowand it is of the order of 10-6 Ω cm.

Due to the absence of the forbidden gap, there is nostructure for holes.

The total current in conductor is simply a flow ofelectrons.

For conductors, the energy gap is of the order of 0.01 eV.

Semiconductors

Semiconductors are materials whose electricalresistivity lies between insulator and conductor. Examplesare silicon (Si), germanium (Ge) ….

The resistivity of semiconductors lie between 10-4 Ω cm to103 Ω cm at room temperature.

At low temperature, the valence band is all most full andconduction band is almost empty. The forbidden gap isvery small equal to 1 eV.

Semiconductor behaves like an insulator at lowtemperature. The most commonly used semiconductor issilicon and its band gap is 1.21 eV and germanium bandgap is 0.785 eV.

When a conductor is heated its resistanceincreases; The atoms vibrate more and theelectrons find it more difficult to move throughthe conductor but, in a semiconductor theresistance decreases with an increase intemperature. Electrons can be excited up to theconduction band and Conductivity increases.

6/18/2014

4

InsulatorsIn insulator, the valence band is full but the

conduction band is totally empty. So, free electrons fromconduction band is not available.

In insulator the energy gap between the valence andconduction band is very large and its approximatelyequal to 5 eV or more.

Hence electrons cannot jump from valence band to theconduction band. So, a very high energy is required topush the electrons to the conduction band.

The electrical conductivity is extremely small.

The resistivity of insulator lie between 103 to 1017 Ωm, atthe room temperature

Examples are plastics, paper …..

Types of semiconductors

Semiconductors

Intrinsic Semiconductor Extrinsic Semiconductor

p - type n - type

Intrinsic Semiconductor

The intrinsic semiconductor are pure semiconductor materials.

These semiconductors posses poor conductivity.

The elemental and compound semiconductor can be intrinsictype.

The energy gap in semiconductor is very small.

So even at the room temperature, some of electrons fromvalance band can jump to the conduction band by thermalenergy.

The jump of electron in conduction band adds one conductionelectron in conduction band and creates a hole in the valenceband. The process is called as “generation of an electron–holepair”.

In pure semiconductor the no. of electrons in conduction bandand holes in holes in valence bands are equal.

Extrinsic Semiconductor

Extrinsic semiconductor is an impure semiconductorformed from an intrinsic semiconductor by adding a smallquantity of impurity atoms called dopants.

The process of adding impurities to the semiconductorcrystal is known as doping.

This added impurity is very small of the order of one atomper million atoms of pure semiconductor.

Depending upon the type of impurity added the extrinsicsemiconductors are classified as:

(1) p – type semiconductor

(2) n – type semiconductor

The application of band theory to n-type and p-type semiconductors shows that extra levels have been addedby the impurities.

In n-type material there are electron energy levels nearthe top of the band gap so that they can be easily excited intothe conduction band.

In p-type material, extra holes in the band gap allowexcitation of valence band electrons, leaving mobile holes in thevalence band.

p – type semiconductor

The addition of trivalent impurities such as boron,aluminum or gallium to an intrinsic semiconductor createsdeficiencies of valence electrons,called "holes". It is typicalto use B2H6 diborane gas to diffuse boron into the siliconmaterial.

http://hyperphysics.phy-astr.gsu.edu/hbase/solids/band.html



http://hyperphysics.phy-astr.gsu.edu/hbase/solids/dope.html







http://hyperphysics.phy-astr.gsu.edu/hbase/solids/intrin.html



6/18/2014

5

n – type semiconductor

The addition of pentavalent impurities such asantimony, arsenic or phosphorous contributes freeelectrons, greatly increasing the conductivity of theintrinsic semiconductor. Phosphorous may be added bydiffusion of phosphine gas (PH3).

Simple Diode (p n- junction Diode)

The two terminals are called Anode and Cathode.

At the instant the two materials are “joined”, electronsand holes near the junction cross over and combine witheach other.

Holes cross from P-side to N-side and Free electrons crossfrom N-side to P-side.

At P-side of junction, negative ions are formed.

At N-side of junction, positive ions are formed.

Depletion region is the region having no freecarriers.

Further movement of electrons and holes acrossthe junction stops due to formation of depletionregion.

Depletion region acts as barrier opposing furtherdiffusion of charge carriers. So diffusion stopswithin no time.

Current through the diode under no-biascondition is zero.

Positive of battery connected to n-type material(cathode).

Negative of battery connected to p-type material(anode).

Reverse bias…..

Free electrons in n-region are drawn towards positive ofbattery, Holes in p-region are drawn towards negative ofbattery.

Depletion region widens, barrier increases for the flow ofmajority carriers.

Majority charge carrier flow reduces to zero.

Minority charge carriers generated thermally can crossthe junction – results in a current called “reversesaturation current” Is , Is is in micro or nano amperes orless. Is does not increase “significantly” with increase inthe reverse bias voltage

Forward bias

Positive of battery connected to p-type (anode)

Negative of battery connected to n-type (cathode)





6/18/2014

6

Forward bias…

Electrons in n-type are forced to recombine withpositive ions near the boundary, similarly holes in p-type are forced to recombine with negative ions.

Depletion region width reduces.

An electron in n-region “sees” a reduced barrier at thejunction and strong attraction for positive potential.

As forward bias is increased, depletion region narrowsdown and finally disappears – leads to exponential risein current.

Forward current is measured in milli amperes

Zener Diode

A diode which is heavily doped and whichoperates in the reverse breakdown region with asharp breakdown voltage is called a Zener diode.

This is similar to the normal diode except thatthe line (bar) representing the cathode is bent atboth side ends like the letter Z for Zener diode.

In simple diode the doping is light; as a result,the breakdown voltage is high and not sharp. But ifdoping is made heavy, then the depletion layersbecomes very narrow and even the breakdownvoltage gets reduced to a sharp value.

Working Principle

The reverse breakdown of a Zener diode mayoccur either due to Zener effect or avalanche effect.But the Zener diode is primarily depends on Zenereffect for its working.

When the electrical field across the junction ishigh due to the applied voltage, the Zenerbreakdown occurs because of breaking of covalentbonds and produces a large number of electronsand holes which constitute a steep rise in thereverse saturation current (Zener current IZ). Thiseffect is called as Zener effect.

Zener current IZ is independent of the appliedvoltage and depends only on the externalresistance.

I-V characteristic of a Zener diode

The forward characteristic is simply that of anordinary forward biased junction diode. Under thereverse bias condition, the breakdown of a junctionoccurs.

Its depends upon amount of doping. It can beseen from above figure as the reverse voltage isincreased the reverse current remains negligiblysmall up to the knee point (K) of the curve.

6/18/2014

7

At point K, the effect of breakdown processbeings. The voltage corresponding to the point Kin figure is called the Zener breakdown voltageor simply Zener voltage (VZ), which is very sharpcompared to a simple p-n junction diode. Beyondthis voltage the reverse current (IZ) increasessharply to a high value.

The Zener diode is not immediately burnt justbecause it has entered the breakdown region.

The Zener voltage VZ remains constant evenwhen Zener current IZ increases greatly.

The maximum value of current is denoted by IZ

max and the minimum current to sustain breakdownis denoted by IZ min. By two points A and B on thereverse VI characteristic, the Zener resistance isgiven by the relation,

rz = ( Δ VZ / Δ IZ) -----(1)

Zener diode Applications:

I. Zener diodes are used as a voltage regulator.

II. They are used in shaping circuits as peaklimiters or clippers.

III. They are used as a fixed reference voltage intransistor biasing and for comparison purpose.

IV. They are used for meter protection againstdamage from accidental application ofexcessive voltage.

6/18/2014

1

LASER

Light Amplification by StimulatedEmission of Radiation

Objectives…

Introduction and understand the principle ofLASER

• Light Amplification by Stimulated Emission ofRadiation

• Absorption

• Spontaneous Emission

• Stimulated Emission

• Population Inversion

• Optical Pumping

Objectives…

Characteristics or Properties of Laser Light

• Coherence

• High Intensity

• High directionality

• High monochromaticity

Laser light is highly powerful and it is capable of propagating over long distances and it is not easily absorbed by water.

Introduction• LASER

“Light Amplification by Stimulated Emissionof Radiation”

• MASER (1939 Towner)

“Microwave Amplification by StimulatedEmission of Radiation”

• Stimulated Emission - Einstein in 1917.

• Ruby Crystal LASER - Maiman, California in 1960.

• He-Ne LASER - Ali Javan in 1961.

• Diode LASER- Hall in 1962.

Light having following Properties

Wavelength

Frequency

Amplitude

Phase

Coherence/Incoherence

Velocity

Direction

Absorption

• E1 = Ground state

• E2 = Excited State

• E = hν (Photon Energy)

6/18/2014

2

• According to Bohr’s law atomic system ischaracterized by discrete energy level.

• When atoms absorb or release energy ittransit upward or downward.

• Lower level E1 & Excited level E2

• So, h ƒ = E2 – E1

• The rate of absorption depends on no. ofatoms N1 present in E1 & spectral energydensity u(ƒ) of radiation

• So, P12 α N1 u(ƒ)

• P12= B12N1 u(ƒ)

Spontaneous Emission

• E1 = Ground State

• E2 = Excited State

• E = E2 – E1

= ΔE

= hν

• System having atoms in excited state.

• Goes to downward transition with emittingphotons, hƒ = E1 – E2.

• Emission is random, so if not in same phasebecomes incoherent.

• The transition depends on atoms in excited stateN2.

P12(spont) α N2 = A21 N2

• Where,

A21 = Einstein coefficient for spontaneousEmission. we get Incoherent radiation forms heatby light amplification of radiation by spontaneousemission.

Stimulated Emission

• System having atoms in excited state.

• Goes to downward transition with emittingphotons.

• 2hƒ = E1 – E2. After applying photon energy hƒ.

• Emission is depends on energy density u(ƒ) & No. ofatoms in excited state N2

• P12(stimul) α u(ƒ) N2 = B21 N2 u(ƒ)

• Where, B21 = Einstein coefficient for StimulatedEmission.

• Thus one photon of energy hƒ stimulates twophotons of energy hƒ in same phase & directions.So, we get coherent light amplification of radiationby stimulated emission.

Population Inversion

• It is the process of increasing exited electrons inhigher energy levels.

• Due to this process the production of laser ispossible.

• The energy level between the ground state E1 (1st

level) and exited state E3 (3rd level) is known asmetastable state E2 (2nd level).

• By optical pumping electrons from ground statejumps to exited state by absorbing photons.

6/18/2014

3

• The electrons remain only for 10-8 sec in exitedstate E3, so most of them jumps back to theground state E1 by emitting photons. But some ofthem jumps to the metastable state E2.

• They (electron) stay in metastable state for more then 10-3 sec.

• So electron density increases in metastable state.

• Thus the transitions are possible it takes more no. of electrons together and ν – (knew)

12 photon beam is produced which constitute laser beam.

Optical PumpingThere are no of techniques for pumping a

collection of atoms to an inverted state.

• Optical pumping

• Electrical discharge

• Direct conversion

When photon of blue green light incident onRuby crystal, electrons from ground state absorbsand exited and jumps on higher energy state levelsand comes back to metastable state. They increasepopulation of electrons in metastable state.

This process is called optical pumping which isdone by flash tube.

Relation between Einstein’s ‘A’ and ‘B’ coefficients

• Einstein obtained a mathematical expression forthe existence of two different kinds of processes,

(1) Spontaneous emission

(2) Stimulated emission

• Consider all atoms r in thermal equilibrium at T.

• Radiation of freq. ƒ & energy density u(ƒ).

• N1 & N2 r atoms in E1 & E2 respectively.

• In equilibrium absorption rates & emission rates must be same.

• i.e. B12 N1 u(ƒ) = A21 N2+ B21 N2 u(ƒ)

A21 N2= u(ƒ) [B12N1 – B21N2]

So, u(f) = [A21 N2 / (B12 N1 – B21 N2)] ---------(1)

------------(2)

• Boltzmann distribution law,

------------(3)

• So, -----------(4)

• But, E2 – E1 = hf -----------(5)

• So, -----------(6)

21

21

12 1

21 2

( )

[ ]

ƒ

1

A

Bu

B N

B N

1

2

/

1 0

/

2 0

E kT

E kT

N N e

N N e

2 1( ) /1

2

E E kTNe

N

h /1

2

ƒ kTNe

N

---------- (7)

• According to plank’s radiation formula,

----------- (8)

• Where, B12 = B21 & A21 / B21 = ------------ (9)

• So, Ratio of spontaneous to stimulated emission:

--------- (10)

21

21

ƒ12

21

h /

ƒ

1

( )

[ ]kT

e

A

Bu

B

B

3

3 ƒh /

8 1( ) ( )

[ ]

ƒƒ

1kT

uc

h

e3

3

8 ƒh

c

2 21 21

2 21 21

3

3

8

( ) ( ) ( )

ƒ

ƒ ƒ ƒ

N A A hR

B u B u ucN

• So,

--------- (11)

--------- (12)

• So, R = ---------- (13)

If hƒ << kT, in thermal equilibrium,

then R = << 1

• hƒ<<kT – Stimulated emission

–Valid in microwave region (MASER)

• hƒ>>kT – Spontaneous emission

–Valid in visible region, incoherent

3

3 /

3

3

ƒh

8( )

8

ƒƒ

&

ƒƒ

1

1( ) ( )

[ ]kT

h

uc

uR

h

e

c

ƒh /1[ ]

kTe

ƒh /1[ ]

kTe

6/18/2014

4

Types of LASER

There are three types of lasers

1. Solid Laser (Ruby Laser)

2. Liquid Laser

3. Gas Laser ( He – Ne Laser, CO2 Laser)

Ruby Laser…To produce laser from solid, Ruby crystal is used.

Ruby is an aluminum oxide crystal (Al2O3) in whichsome of the aluminum atoms have been replacedwith Cr+3 chromium atoms (0.05% by weight).

It was the first type of laser invented, and was firstoperated by Maiman in Research Laboratories on1960.

Chromium gives ruby its characteristic pink or redcolor by absorbing green and blue light.

For a ruby laser, a crystal of ruby is formed into acylinder. The ruby laser is used as a pulsed laser,producing red light at 6943 Å.

Ruby crystal is surrounded by xenon tube. Rubycrystal is fully silvered at one side and partiallysilvered at the other end.

A strong beam of blue green light is made to fall upon crystal from xenon tube and this light isabsorbed by the crystal.

Because of this, many electrons from ground stateor normal state are raised to the excited state orhigher state and electron falls to metastable state.

During this transition photon is not emitted butexcess energy of the electrons absorbed in crystallattice.

As electron drops to metastable state they remainthere for certain time ~ 10-6 sec.

Thus the incident blue green light from tubeincreases the number of electron in metastablestate and then the population inversion can beachieved.

If a light of different frequency is allowed to fallon this material, the electrons move back andforth between silvered ends of the crystal.

While moving through they get stimulated andexiced electrons radiate energy.

6/18/2014

5

Thus readia photon has the same frequency asthat of incident photon and is also in exactly samephase.

When the intensity of light beam is increased thesame process is repeated.

Finally extremely intensified beam of light energiesfrom the semi silvered side of the crystal.

This way it is possible to get extremely intensifiedand coherent beam of light from the crystal. Thisbeam is nothing but higher energetic beam – ie.LASER beam.

Applications of Ruby Laser…Ruby lasers have declined in use with the

discovery of better lasing media. They are still usedin a number of applications where short pulses ofred light are required. Holography's around theworld produce holographic portraits with rubylasers, in sizes up to a meter squared.

Many non-destructive testing labs use ruby lasersto create holograms of large objects such asaircraft tires to look for weaknesses in the lining.

Ruby lasers were used extensively in tattoo andhair removal.

Drawbacks of Ruby Laser…• The laser requires high pumping power because

the laser transition terminates at the ground stateand more than half of ground state atoms must bepumped to higher state to achieve populationinversion.

• The efficiency of ruby laser is very low becauseonly green component of the pumping light is usedwhile the rest of components are left unused.

• The laser output is not continues but occurs in theform of pulses of microseconds duration.

• The defects due to crystalline imperfections arealso present in this laser.

Gaseous Laser (He – Ne Laser)A helium - neon laser, usually called a He-Ne laser,

is a type of small gas laser. He-Ne lasers have manyindustrial and scientific uses, and are often used inlaboratory demonstrations of optics.

He-Ne laser is an atomic laser which employs afour-level pumping scheme.

The active medium is a mixture of 10 parts ofhelium to 1 part of neon.

Neon atoms are centers and have energy levelssuitable for laser transitions while helium atomshelp efficient excitation of neon atoms.

The most common wavelength is 6328 Å. Theselasers produced powers in the range 0.5 to 50 mWin the red portion of the visible spectrum.

They have long operating life of the order of50,000 hrs.

Construction…

It consists of a glass discharge tube of abouttypically 30 cm long and 1.5 cm diameter.

The tube is filled with a mixture of helium andneon gases in the 10:1.

Electrodes are provided in the tube to produce adischarge in the gas.

They are connected to a high voltage powersupply. The tube is hermetically sealed with glasswindows oriented at Brewster angle to the tube.The cavity mirrors are arranged externally.

6/18/2014

6

Working…When the power is switched on , a high voltage of

about 10 kV is applied across the gas.

It is sufficient to ionize the gas.

The electrons and ions are produced in the process ofdischarge are accelerated toward the anode andcathode respectively.

The electron have a smaller mass, they acquire ahigher velocity. They transfer their kinetic energy tohelium atoms through inelastic collisions.

The initial excitation effects only the helium atoms.They are in metastable state and cannot return inground state by the spontaneous emission.

The excited helium atoms can return to the ground stateby transforming their energy to neon atoms throughcollision. This transformation take place when twocolliding atoms have initial energy state. It is calledresonant transfer of energy.

So, the pumping mechanism of He-Ne Laser is when thehelium atom in the metastable state collides with neonatom in the ground state the neon atom is excited andthe helium atom drops back to the ground state.

The role of helium atom is thus to excite neon atom andcause, population inversion. The probability of energytransfer from helium atoms to neon atoms is more asthere are 10 atoms of helium per 1 neon atom in gasmixture.

Without the Brewster windows, the light output isunpolarized, because of it laser output to belinearly polarized.

When the excited Ne atom passes from metastablestate (3s) to lower level (2p), it emits photon ofwavelength 632 nm.

This photon travels through the gas mixtureparallel to the axis of tube, it is reflected back andforth by the mirror ends until it stimulates anexcited Ne atom and causes it to emit a photon of632nm with the stimulating photon.

The stimulated transition from (3s) level to (2p)level is laser transition.

Although 6328 Å is standard wavelength of He-NeLaser, other visible wavelengths 5430 Å (Green)5940 Å (yellow-orange), 6120 Å (red-orange) canalso produced.

Overall gain is very low and is typically about 0.010% to 0.1 %.

The laser is simple practical and less expensive.

The Laser beam is highly collimated, coherent andmonochromatic.

Applications of He-Ne Laser…

The Narrow red beam of He-Ne laser is used insupermarkets to read bar codes.

The He-Ne Laser is used in Holography inproducing the 3D images of objects.

He-Ne lasers have many industrial and scientificuses, and are often used in laboratorydemonstrations of optics.

6/18/2014

7

Semiconductor Laser (Diode Laser)• A semiconductor laser is a laser in which a

semiconductor serves as a photon source.

• The most common semiconductor material thathas been used in lasers is gallium arsenide.

• Einstein’s Photoelectric theory states that lightshould be understood as discrete lumps of energy(photons) and it takes only a single photon withhigh enough energy to knock an electron loosefrom the atom it's bound to.

• Stimulated, organized photon emission occurswhen two electrons with the same energy andphase meet. The two photons leave with thesame frequency and direction.

P type Semiconductors

• In the compound GaAs, each Ga atom has threeelectrons in its outermost shell of electrons andeach As atom has five.

• When a trace of an impurity element with twoouter electrons, such as Zn (zinc), is added to thecrystal.

• The result is the shortage of one electron from oneof the pairs, causing an imbalance in which there isa “hole” for an electron but there is no electronavailable.

• This forms a p-type semiconductor.

N type Semiconductors• When a trace of an impurity element with six

outer electrons, such as Se (selenium), is addedto a crystal of GaAs, it provides on additionalelectron which is not needed for the bonding.

• This electron can be free to move through thecrystal.

• Thus, it provides a mechanism for electricalconductivity.

• This type is called an n-type semiconductor.

• Under forward bias (the p-type side is madepositive) the majority carriers, electrons in the n-side, holes in the p-side, are injected across thedepletion region in both directions to create apopulation inversion in a narrow active region. Thelight produced by radioactive recombination acrossthe band gap is confined in this active region.

Application of Lasers…

Laser beam is used to measure distances of sun,moon, stars and satellites very accurately.

It can be used for measuring velocity of light, tostudy spectrum of matters, to study Ramaneffect.

It can be is used for increasing speed andefficiency of computer.

It is used for welding.

It is used in biomedical science.

It is used in 3D photography.

Application of Lasers…

It is used for communication, T. V. transmission,to search the objects under sea.

It can be used to predict earthquake. Laser tools are used in surgery. It is used for detection and treatment of cancer. It is used to aline straight line for construction of

dam, tunnels etc. It is used in holography. It is used in fiber optic communication. It is also used in military, like LIDAR. It is used to accelerate some chemical reactions.

6/18/2014

1

Special

Theory

of Relativity

The dependence of various physical phenomena on

relative motion of the observer and the observed

objects, especially regarding the nature and behaviour

of light, space, time, and gravity is called relativity.

When we have two things and if we want to find out

the relation between their physical property

i.e.velocity,accleration then we need relation between

them that which is higher and which is lower.In

general way we reffered it to as a relativity.

The famous scientist Einstein has firstly found out the

theory of relativity and he has given very useful

theories in relativity.

Introduction to Relativity

What is Special Relativity?

In 1905, Albert Einstein determined that the laws

of physics are the same for all non-accelerating

observers, and that the speed of light in a vacuum

was independent of the motion of all observers.

This was the theory of special relativity.

FRAMES OF REFERENCE

A Reference Frame is the point of View, from which we Observe an Object.

A Reference Frame is the Observer it self, as the Velocity and acceleration are common in Both.

Co-ordinate system is known as FRAMES OF REFERENCE

Two types:

1. Inertial Frames Of Reference.

2. non-inertial frame of reference.

FRAMES OF REFERENCE

We have already come across idea of frames of

reference that move with constant velocity. In

such frames, Newton’s law’s (esp. N1) hold.

These are called inertial frames of reference.

Suppose you are in an accelerating car looking at a

freely moving object (I.e., one with no forces

acting on it). You will see its velocity changing

because you are accelerating! In accelerating

frames of reference, N1 doesn’t hold – this is a

non-inertial frame of reference.

6/18/2014

2

Conditions of the Galilean Transformation

Parallel axes (for convenience)

K’ has a constant relative velocity in the x-direction with

respect to K

Time (t) for all observers is a

Fundamental invariant,

i.e., the same for all inertial observers

speed of frame

NOT speed of object

x ' x – v t

y ' y

z ' z

Galilean TransformGalilean Transformation Inverse Relations

Step 1. Replace with .

Step 2. Replace ―primed‖ quantities with

―unprimed‖ and ―unprimed‖ with ―primed.‖

speed of frame

NOT speed of object

x x’ vt

y y’

z z’

t t’

General Galilean Transformations

'

'

'

tt

yy

vtxx

11'

''

''

'

dt

dt

dt

dt

vvdt

dy

dt

dy

vvvvdt

dx

dt

dx

samethearetandt

yy

xx

yy

yy

xx

xx

aadt

dv

dt

dv

aadt

dv

dt

dv

samethearetandt

''

'0'

'

inertial reference frame

FamFam '

11'

''

''

'

dt

dt

dt

dt

ttdt

dy

dt

dy

vuuvdt

dx

dt

dx

samethearetandt

yy

xx

frame K frame K’

Newton’s Eqn of Motion is same at

face-value in both reference frames

Posi

tion

Vel

ocit

yA

ccel

erat

ion

Einstein’s postulates of special theory of

relativity

• The First Postulate of Special Relativity

The first postulate of special relativity states

that all the laws of nature are the same in all

uniformly moving frames of reference.

Einstein reasoned all motion is relative and all frames of

reference are arbitrary.

A spaceship, for example, cannot measure its speed

relative to empty space, but only relative to other objects.

Spaceman A considers himself at rest and sees

spacewoman B pass by, while spacewoman B considers

herself at rest and sees spaceman A pass by.

Spaceman A and spacewoman B will both observe only the

relative motion.

The First Postulate of Special Relativity

A person playing pool

on a smooth and fast-

moving ship does not

have to compensate

for the ship’s speed.

The laws of physics

are the same whether

the ship is moving

uniformly or at rest.


6/18/2014

3

Einstein’s first postulate of special relativity

assumes our inability to detect a state of

uniform motion.

Many experiments can detect accelerated

motion, but none can, according to Einstein,

detect the state of uniform motion.


The second postulate of special relativity

states that the speed of light in empty space

will always have the same value regardless

of the motion of the source or the motion of

the observer.

The Second Postulate of Special Relativity

Einstein concluded that if an

observer could travel close to

the speed of light, he would

measure the light as moving

away at 300,000 km/s.

Einstein’s second postulate of

special relativity assumes that

the speed of light is constant.


The speed of light is constant regardless of the

speed of the flashlight or observer.


The speed of light in all reference frames is always the

same.

• Consider, for example, a spaceship departing from the

space station.

• A flash of light is emitted from the station at 300,000

km/s—a speed we’ll call c.

The speed of a light flash emitted by either the

spaceship or the space station is measured as c by

observers on the ship or the space station.

Everyone who measures the speed of light will get

the same value, c.


18

The Ether: Historical Perspective

Light is a wave.

Waves require a medium through which to

propagate.

Medium as called the ―ether.‖ (from the Greek

aither, meaning upper air)

Maxwell’s equations assume that light obeys

the Newtonian-Galilean transformation.

6/18/2014

4

The Ether: Since mechanical waves require a

medium to propagate, it was generally accepted that light

also require a medium. This medium, called the ether,

was assumed to pervade all mater and space in the

universe.

20

The Michelson-Morley Experiment

Experiment designed to measure small changes in the speed of light was performed by Albert A. Michelson (1852 – 1931, Nobel ) and Edward W. Morley (1838 –1923).

Used an optical instrument called an interferometer that Michelson invented.

Device was to detect the presence of the ether.

Outcome of the experiment was negative, thus contradicting the ether hypothesis.

Michelson-Morley Experiment(1887)

Michelson developed a device called an inferometer.

Device sensitive enough to detect the ether.


Apparatus at rest wrt the ether.


Light from a source is split by a half silvered mirror (M)

The two rays move in mutually perpendicular directions


The rays are reflected by two mirrors (M1 and M2)

back to M where they recombine.

The combined rays are observed at T.

6/18/2014

5


The path distance for each ray is the same (l1=l2).

Therefore no interference will be observed


Apparatus at moving through the ether.

u

ut


First consider the time required for the parallel ray

Distance moved during the first part of the path is

|| ||

||

ct L ut

Lt

(c u )

(distance moved by

light to meet the mirror)

u

ut


(distance moved by light to meet the mirror))(||

uc

Lt

||||utLct

Similarly the time for the return trip is )(

||uc

Lt

The total time

)()(||

uc

L

uc

Lt

u

ut


The total time ||

2 2

2 2

( ) ( )

2

( )

2 /

1

L Lt

c u c u

Lc

c u

L c

u c

u

ut

Michelson-Morley Experiment(1887)For the perpendicular ray

we can write,

ct

vt

2 2 2

2 2 2 2 2

2 2 2

2 2

( )

( )

ct L ut

L c t u t

c u t

Lt

c u

(initial leg of the path)

The return path is the same as the

initial leg therefore the total time is

22

2

uc

Lt

u

ut

6/18/2014

6


ct

vt

2 2

2 2

2

2 /

1

Lt

c u

L ct

u c

The time difference between the

two rays is,1

21

2 2

|| 2 2

2 2

2 3

21 1

2

2

L u ut t t

c c c

After a binom ial expansi

L u Lut

c c c

on

u

ut

Michelson-Morley Experiment(1887) The expected time difference is too small to be measured

directly!

Instead of measuring time, Michelson and Morley looked for a fringe change.

as the mirror (M) was rotated there should be a shift in the interference fringes.

Results of the Experiment

A NULL RESULT

No time difference was found!

Hence no shift in the interference patterns

Conclusion from Michelson-Morley Experiment the ether didn’t exist.

The Lorentz Transformation

We are now ready to derive the correct transformation

equations between two inertial frames in Special

Relativity, which modify the Galilean Transformation.

We consider two inertial frames S and S’, which have a

relative velocity v between them along the x-axis.

x

y

z

S

x'

y'

z '

S' v

Now suppose that there is a single flash at the origin of S and S’ at

time , when the two inertial frames happen to coincide. The

outgoing light wave will be spherical in shape moving outward

with a velocity c in both S and S’ by Einstein’s Second Postulate.

We expect that the orthogonal coordinates will not be affected by

the horizontal velocity:

But the x coordinates will be affected. We assume it will be a

linear transformation:

But in Relativity the transformation equations should have the

same form (the laws of physics must be the same). Only the

relative velocity matters. So

x y z c t

x y z c t

2 2 2 2 2

2 2 2 2 2

y y

z z

x k x vt

x k x vt

a fa f

k k

Consider the outgoing light wave along the x-axis

(y = z = 0).

Now plug these into the transformation equations:

Plug these two equations into the light wave equation:

x ct

x ct

in fram e S '

in fram e S

1 / &

1 /

x k x vt k ct vt kct v c

x k x vt k ct vt kct v c

ct x kct v c

ct x kct v c

t kt v c

t kt v c

1

1

1

1

/

/

/

/

a fa f

a fa f

Plug t’ into the equation for t:

So the modified transformation equations for the

spatial coordinates are:

Now what about time?

t k t v c v c

k v c

kv c

2

2 2 2

2 2

1 1

1 1

1

1

/ /

/

/

a fa fc h

x x vt

y y

z z

a f

x x vt

x x vt

x x vt vt

a fa f

a f

inverse transform ation

Plug one into the other:

6/18/2014

7

Solve for t’:

So the correct transformation (and inverse transformation)

equations are:

2 2

2 2

2 2

2

2 2

2 2 2 2

2 2 2 2

2

1

1 / 1

1 /

/

1/

/

x x vt vt

x vt vt

v cx vt vt

v c

xv c vt vt

t xv c vtv

t t vx c

x x vt x x vt

y y y y

z z z z

t t vx c t t vx c

a f a f

c h c h

/ /2 2

The Lorentz Transformation

Application of Lorentz Transformation Time Dilation

We explore the rate of time in different inertial frames by considering a special kind of clock – a light clock – which is just one arm of an interferometer. Consider a light pulse bouncing vertically between two mirrors. We analyze the time it takes for the light pulse to complete a round trip both in the rest frame of the clock (labeled S’), and in an inertial frame where the clock is observed to move horizontally at a velocity v (labeled S).

In the rest frame S’

tL

c

tL

c

t tL

c

1

2

1 2

2

= tim e up

= tim e dow n

=

m irror

m irror

L

Now put the light clock on a spaceship, but measure the

roundtrip time of the light pulse from the Earth frame S:

tt

tt

c

L v t c t

L c v t

tL

c v

tL

c v c v c

1

2

2 2 2 2 2

2 2 2 2

2

2

2 2

2 2 2 2

2

2

4 4

4

4

2 1

1 1

tim e up

tim e dow n

The speed of light is still in this fram e, so

/ /

/

/ /

c h

L

c t / 2

v t / 2

So the time it takes the light pulse to make a roundtrip in

the clock when it is moving by us is appears longer than

when it is at rest. We say that time is dilated. It also doesn’t

matter which frame is the Earth and which is the clock. Any

object that moves by with a significant velocity appears to

have a clock running slow. We summarize this effect in the

following relation:

2 2

1 2 , 1,

1 /

Lt

cv c

Length Contraction

Now consider using a light clock to measure the length of an

interferometer arm. In particular, let’s measure the length along

the direction of motion.

In the rest frame S’:

Now put the light clock on a spaceship, but measure the roundtrip

time of the light pulse from the Earth frame S:

Lc

02

1 2

1 2

1 1 1

2 2 2

time out, tim e back

t t

t t t

LL vt ct t

c v

LL vt ct t

c v

A A’ C C’

vt1 L

In other words, the length of the interferometer arm appears contracted when it moves by us. This is known as the Lorentz-Fitzgerald contraction. It is closely related to time dilation. In fact, one implies the other, since we used time dilation to derive length contraction.

1 2 2 2 2 2

2 2

2 2

0

2 2

2 2 1

1 /

1 /2

But, from tim e dilation

1 /

1 1

1 /

Lc Lt t t

c v c v c

ctL v c

t

v c

LL

v c

6/18/2014

8

Engineering physics By Dr. M N Avadhnulu, S

Chand publication

ENGINEERING PHYSICS

ABHIJIT NAYAK

http://www.maths.tcd.ie/~cblair/notes/specrel.pdf

http://www.newagepublishers.com/samplechapter/0

00485.pdf

http://www.maths.tcd.ie/~cblair/notes/specrel.pdf

http://www.newagepublishers.com/samplechapter/000485.pdf


6/18/2014

1

Superconductivity

Introduction of superconductivity

• Electrical resistivity ↓ Temp. ↓

• 0 º K Electrical resistivity is 0 for perfectly pure

metal

• Any metal can’t be perfectly pure.

• The more impure the metal Electrical resistivity ↑

• Certain metals when they cooled their electrical

resistivity decreases but at Tc resistivity is 0 this

state of metal is called __________.

• Finder – K Onnes 1911

Properties of Superconductors

Electrical Resistance

• Zero Electrical Resistance

• Defining Property

• Critical Temperature

• Quickest test

• 10-5Ωcm

Effect of Magnetic Field

Critical magnetic field (HC) –

Minimum magnetic field

required to destroy the

superconducting property at

any temperature

H0 – Critical field at 0K

T - Temperature below TC

TC - Transition Temperature

Element HC at 0K

(mT)

Nb 198

Pb 80.3

Sn 30.9

Superconducting

Normal

T (K) TC

H0

HC

2

C 0

C

TH H 1

T

Effect of Electric Current

• Large electric current – induces magnetic field – destroys superconductivity

• Induced Critical Current iC = 2πrHC

Persistent Current

• Steady current which flows through a superconducting ring without any decrease in strength even after the removal of the field

• Diamagnetic property

i

Meissner effect

• When Superconducting material cooled bellow its Tc it

becomes resistenceless & perfect diamagnetic.

• When superconductor placed inside a magnetic field in

Tc all magnetic flux is expelled out of it the effect is

called Meissner effect.

• Perfect diamagnetism arises

from some special magnetic

property of Superconductor.

6/18/2014

2

• If there is no magnetic field inside the superconductor

relative permeability or diamagnetic constant μr =0.

• Total magnetic induction B is,

• If magnetic induction B=0 then,

0( )B H M

00 ( )H M

M H

1m

M

H

Magnetic Flux Quantisation

• Magnetic flux enclosed in a superconducting ring =integral multiples of fluxon

• Φ = nh/2e = n Φ0 (Φ0 = 2x10-15Wb)

Effect of Pressure

• Pressure ↑, TC ↑

• High TC superconductors – High pressure

Thermal Properties

• Entropy & Specific heat ↓ at TC

• Disappearance of thermo electric effect at TC

• Thermal conductivity ↓ at TC – Type Isuperconductors

Stress

• Stress ↑, dimension ↑, TC ↑, HC affected

Frequency

• Frequency ↑, Zero resistance – modified, TC not affected

Impurities

• Magnetic properties affected

Size

• Size < 10-4cm – superconducting state modified

General Properties

• No change in crystal structure

• No change in elastic & photo-electric properties

• No change in volume at TC in the absence of magnetic field

Isotope Effect

• Maxwell

• TC = Constant / Mα

• TC Mα = Constant (α – Isotope Effect coefficient)

• α = 0.15 – 0.5

• α = 0 (No isotope effect)

• TC√M = constant

Classification & characterization of super

conductor

• Type I or soft super conductor

– Exhibit complete Meissner effect.

– Bellow Hc super conductor above Hc Normal

– Value of Hc is order of 0.1 T.

– Aluminum, lead & Indium are type I super conductor

– Not used as strong electromagnets

• Type II or Hard super conductor

– Exhibit complete Meissner effect bellow a certain

critical field Hc1 at this point diamagnetism &

superconductivity ↓. This state is mix state called

vortex state.

– At certain critical field Hc2 superconductivity

disappears.

– Niobium, Aluminum, silicon, ceramic are type II

superconductors.

– Pb is type I superconductor ac Hc =600 gauss at 4º K

when a small impurity of In is added it becomes type

II superconductor with Hc1 =400 gauss & Hc2 =1000

gauss.

6/18/2014

3

Types of Superconductors

Type I

• Sudden loss of

magnetisation

• Exhibit Meissner Effect

• One HC = 0.1 tesla

• No mixed state

• Soft superconductor

• Eg.s – Pb, Sn, Hg

Type II

• Gradual loss of magnetisation

• Does not exhibit complete

Meissner Effect

• Two HCs – HC1 & HC2 (≈30

tesla)

• Mixed state present

• Hard superconductor

• Eg.s – Nb-Sn, Nb-Ti-M

HHC

Superconducting

Normal

Superconducting

-M

Normal

Mixed

HC1 HCHC2

H

London equation

• According to London’s theory there are two type of

electrons in SC

– Super electrons

– Normal electrons

At 0º K there are only Super electrons.

With increasing temp. Super electrons ↓ Normal electrons

↑ .

Let nn, un & ns, us are no. density & drift velocity of

normal electrons & super electrons respectively.

Equation of motion of Super electrons under

electric field is

• Now current & drift velocity are related as

sdu

m eEdt

2

( )

s s s

s s s

s

s

s

s

s

s s

I n eAu

J n eu

Ju

n e

Jd

n ee E

dt

n e Ed J

dt mLondon's first equation

• London's first equation gives absence of resistance. If E =0 then

• Now from Maxwell's eqn0

sdJ

dt

( )

d BE

dt

B A

d AE

dt

d AE

dt

d AE

dt

2

2

2

2

2

2

( )

( )

s s

s

s

s

s

s

s

s

s

ss

n e Ed J

dt m

d J mE

dt n e

d J m d A

dt n e dt

d m d AJ

dt n e dt

mJ A

n e

n eJ A

m

London's second equation

• Again from ampere Law

Take curl on both sides

0

2

0( )

s

s

B J

n eB A

m

2

0

2

2

2

0

( )

&

( )

s

s

n eB A

m

N ow

B B B A B

n eB B B

m

A B

6/18/2014

4

2

2

0

2

0 2

2

2

2

2

( ) 0

1

1

10

s

s

So B A

n eB B

m

n eAssum e

m

B B

or

B B

λ is called London penetration depth

Elements of BCS Theory

• BCS Theory of Superconductivity

• The properties of Type I superconductors were modeled

successfully by the efforts of John Bardeen, Leon Cooper, and

Robert Schrieffer in what is commonly called the BCS theory.

• A key conceptual element in this theory is the pairing of

electrons close to the Fermi level into Cooper pairs through

interaction with the crystal lattice.

• This pairing results form a slight attraction between the

electrons related to lattice vibrations; the coupling to the

lattice is called a phonon interaction.

• Pairs of electrons can behave very differently from single

electrons which are fermions and must obey the Pauli

exclusion principle.

• The pairs of electrons act more like bosons which can

condense into the same energy level.

• The electron pairs have a slightly lower energy and leave

an energy gap above them on the order of 0.001eV which

inhibits the kind of collision interactions which lead to

ordinary resistivity.

• For temperatures such that the thermal energy is less than

the band gap, the material exhibits zero resistivity.

• Bardeen, Cooper, and Schrieffer received the Nobel

Prize in 1972 for the development of the theory of

superconductivity.

• Cooper Pairs

• The transition of a metal from the normal to the

superconducting state has the nature of a condensation of

the electrons into a state which leaves a band gap above

them.

• This kind of condensation is seen with super fluid helium,

but helium is made up of bosons -- multiple electrons can't

collect into a single state because of the Pauli exclusion

principle.

• Froehlich was first to suggest that the electrons act as pairs

coupled by lattice vibrations in the material.

• This coupling is viewed as an exchange of phonons,

phonons being the quanta of lattice vibration energy.

• Experimental corroboration of an interaction with the

lattice was provided by the isotope effect on the

superconducting transition temperature.

• The boson-like behavior of such electron pairs was

further investigated by Cooper and they are called

"Cooper pairs".

• The condensation of Cooper pairs is the foundation of

the BCS theory of superconductivity.

6/18/2014

5

• In the normal state of a metal, electrons move

independently, whereas in the BCS state, they are bound

into "Cooper pairs" by the attractive interaction. The

BCS formalism is based on the "reduced" potential for

the electrons attraction.

• You have to provide energy equal to the 'energy gap' to

break a pair, to break one pair you have to change

energies of all other pairs.

• This is unlike the normal metal, in which the state of an

electron can be changed by adding a arbitrary small

amount of energy.

• The energy gap is highest at low temperatures but does

not exist at temperatures higher than the transition

temperature.

• The BCS theory gives an expression of how the gap grows

with the strength of attractive interaction and density of

states.

• The BCS theory gives the expression of the energy gap

that depends on the Temperature T and the Critical

Temperature Tc and is independent of the material:

APPLICATIONSOF

SUPER CONDUCTORS

1. Engineering

• Transmission of power

• Switching devices

• Sensitive electrical instruments

• Memory (or) storage element in computers.

• Manufacture of electrical generators and transformers

2. Medical

•Nuclear Magnetic Resonance (NMR)

•Diagnosis of brain tumor

•Magneto – hydrodynamic power generation

JOSEPHSON DEVICESby Brian Josephson

Principle: persistent current in d.c. voltage

Explanation:

• Consists of thin layer of insulating material placed between two superconducting materials.

• Insulator acts as a barrier to the flow of electrons.

• When voltage applied current flowing between super conductors by tunneling effect.

• Quantum tunnelling occurs when a particle moves through a space in a manner forbidden by classical physics, due to the potential barrier involved

6/18/2014

6

Components of current

• In relation to the BCS theory (Bardeen Cooper

Schrieffer) mentioned earlier, pairs of electrons move

through this barrier continuing the superconducting

current. This is known as the dc current.

• Current component persists only till the external

voltage application. This is ac current.

Josephson junctions

• A type of electronic circuit

capable of switching at very

high speeds when operated at

temperatures approaching

absolute zero.

• Named for the British

physicist who designed it,

• a Josephson junction exploits

the phenomenon of

superconductivity.

Construction• A Josephson junction is made

up of two superconductors, separated by a nonsuperconducting layer so thin that electrons can cross through the insulating barrier.

• The flow of current between the superconductors in the absence of an applied voltage is called a Josephson current,

• the movement of electrons across the barrier is known as Josephson tunneling.

• Two or more junctions joined by superconducting paths form what is called a Josephson interferometer.

Construction :

Consists of

superconducting

ring having

magnetic fields of

quantum

values(1,2,3..)

Placed in between

the two Josephson

junctions

Explanation :

• When the magnetic field is applied perpendicular to

the ring current is induced at the two junctions

• Induced current flows around the ring thereby

magnetic flux in the ring has quantum value of field

applied

• Therefore used to detect the variation of very minute

magnetic signals

Uses of Josephson devices

• Magnetic Sensors

• Gradiometers

• Oscilloscopes

• Decoders

• Analogue to Digital converters

• Oscillators

• Microwave amplifiers

• Sensors for biomedical, scientific and defencepurposes

• Digital circuit development for Integrated circuits

• Microprocessors

• Random Access Memories (RAMs)

6/18/2014

7

SQUIDS

(Super conducting Quantum Interference Devices)Discovery:

The DC SQUID was invented in 1964 by Robert

Jaklevic, John Lambe, Arnold Silver, and James

Mercereau of Ford Research Labs

Principle :

Small change in magnetic field, produces variation in

the flux quantum.

Construction:

The superconducting quantum interference device

(SQUID) consists of two superconductors separated by

thin insulating layers to form two parallel Josephson

junctions.

Types

Two main types of SQUID:

1) RF SQUIDs have only one Josephson

junction

2)DC SQUIDs have two or more junctions.

Thereby,

• more difficult and expensive to produce.

• much more sensitive.

Fabrication • Lead or pure niobium The lead is usually in the form

of an alloy with 10% gold or indium, as pure lead is unstable when its temperature is repeatedly changed.

• The base electrode of the SQUID is made of a very thin niobium layer

• The tunnel barrier is oxidized onto this niobium surface.

• The top electrode is a layer of lead alloy deposited on top of the other two, forming a sandwich arrangement.

• To achieve the necessary superconducting characteristics, the entire device is then cooled to within a few degrees of absolute zero with liquid helium

Uses

• Storage device for magnetic flux

• Study of earthquakes

• Removing paramagnetic impurities

• Detection of magnetic signals from brain, heart etc.

Cryotron

The cryotron is a switch that operates using superconductivity. The cryotron works on the principle that magnetic fields destroy superconductivity. The cryotron is a piece of tantalum wrapped with a coil of niobium placed in a liquid helium bath. When the current flows through the tantalum wire it is superconducting, but when a current flows through the niobium a magnetic field is produced. This destroys the superconductivity which makes the current slow down or stop.

6/18/2014

8

Magnetic Levitated Train

Principle: Electro-magnetic induction

Introduction:

Magnetic levitation transport, or maglev, is a form of

transportation that suspends, guides and propels

vehicles via electromagnetic force. This method can be

faster than wheeled mass transit systems, potentially

reaching velocities comparable to turboprop and jet

aircraft (500 to 580 km/h).

• Superconductors may be considered perfect diamagnets

(μr = 0), completely expelling magnetic fields due to the

Meissner effect.

• The levitation of the magnet is stabilized due to flux

pinning within the superconductor.

• This principle is exploited by EDS (Electrodynamic

suspension) magnetic levitation trains.

•In trains where the weight of the large electromagnet is a

major design issue (a very strong magnetic field is required

to levitate a massive train) superconductors are used for the

electromagnet, since they can produce a stronger magnetic

field for the same weight.

Why superconductor ?

How to use a Super conductor

• Electrodynamics suspension

• In Electrodynamic suspension (EDS), both the rail and the train

exert a magnetic field, and the train is levitated by the repulsive

force between these magnetic fields.

• The magnetic field in the train is produced by either

electromagnets or by an array of permanent magnets.

• The repulsive force in the track is created by an induced

magnetic field in wires or other conducting strips in the track.

• At slow speeds, the current induced in these coils and the

resultant magnetic flux is not large enough to support the weight

of the train.

• For this reason the train must have wheels or some other form of

landing gear to support the train until it reaches a speed that can

sustain levitation.

• Propulsion coils on the guide way are used to exert a

force on the magnets in the train and make the train

move forwards.

• The propulsion coils that exert a force on the train are

effectively a linear motor: An alternating current

flowing through the coils generates a continuously

varying magnetic field that moves forward along the

track.

• The frequency of the alternating current is

synchronized to match the speed of the train.

• The offset between the field exerted by magnets on the

train and the applied field create a force moving the

train forward.

Advantages

No need of initial energy in case of magnets for low speeds

One liter of Liquid nitrogen costs less than one liter of mineral

water

Onboard magnets and large margin between rail and train

enable highest recorded train speeds (581 km/h) and heavy load

capacity. Successful operations using high temperature

superconductors in its onboard magnets, cooled with inexpensive

liquid nitrogen

Magnetic fields inside and outside the vehicle are insignificant;

proven, commercially available technology that can attain very

high speeds (500 km/h); no wheels or secondary propulsion

system needed

Free of friction as it is “Levitating”

6/18/2014

9

Engineering physics By Dr. M N Avadhnulu, S Chand publication

Engineering physics by G Vijayakumari

http://www.cengage.com/resource_uploads/static_resources/0534493394/4891/SerwayCh12-

Superconductivity.pdf

https://www.repository.cam.ac.uk/bitstream/handle/1810/34597/Chapter%201.pdf?sequence=5

http://chabanoiscedric.tripod.com/NSCHSS.PDF

http://www.physics.usyd.edu.au/~khachan/PTF/Superconductivity.pdf

http://www.cengage.com/resource_uploads/static_resources/0534493394/4891/SerwayCh12-Superconductivity.pdf




https://www.repository.cam.ac.uk/bitstream/handle/1810/34597/Chapter 1.pdf?sequence=5

https://www.repository.cam.ac.uk/bitstream/handle/1810/34597/Chapter 1.pdf?sequence=5

http://chabanoiscedric.tripod.com/NSCHSS.PDF



1

Atomic

Physics

• “Classical Physics”:

– developed in 15th to 20th century;

– provides very successful description of “every day,

ordinary objects”

• motion of trains, cars, bullets,….

• orbit of moon, planets

• how an engine works,..

• subfields: mechanics, thermodynamics, electrodynamics,

• Quantum Physics:

• developed early 20th century, in response to

shortcomings of classical physics in describing certain

phenomena (blackbody radiation, photoelectric effect,

emission and absorption spectra…)

• describes “small” objects (e.g. atoms )

Quantum Physics

• QP is “weird and counterintuitive”

• “Those who are not shocked when they first come

across quantum theory cannot possibly have

understood it” (Niles Bohr)

• “Nobody feels perfectly comfortable with it “

(Murray Gell-Mann)

• “I can safely say that nobody understands quantum

mechanics” (Richard Feynman) BUT…

• QM is the most successful theory ever developed by

humanity underlies our understanding of atoms,

molecules, condensed matter, nuclei, elementary

particles

• Crucial ingredient in understanding of stars, …

Features of QP

• Quantum physics is basically the recognition that there is less difference between waves and particles than was thought before

• key insights:• light can behave like a particle

• particles (e.g. electrons) are indistinguishable

• particles can behave like waves (or wave packets)

• waves gain or lose energy only in "quantized amounts“

• detection (measurement) of a particle wave will change suddenly into a new wave

• quantum mechanical interference – amplitudes add

• QP is intrinsically probabilistic

• what you can measure is what you can know

WAVE-PICTURE OF RADIATION—

ENERGY FLOW I S CONTI N UOUS

• Radio waves, microwaves, heat waves, light waves, UV-

rays, x-rays and y-rays belong to the family of

electromagnetic waves. All of them are known as

radiation.

• Electromagnetic waves consist of varying electric and

magnetic fields traveling at the velocity of 'c'. The

propagation of electromagnetic waves and their

interaction with matter can be explained with the help of

Maxwell's electromagnetic theory.

• Maxwell's theory treated the emission of radiation by a

source as a continuous process.

• A heated body may be assumed to be capable of giving

out energy that travels in the form of waves of all

possible wavelengths.

• In the same way, the radiation incident on a body was

thought to be absorbed at all possible wavelengths.

• The intensity of radiation is given by,

I = 1E12

where E is the amplitude of the electromagnetic wave.

2

• The phenomena of interference, diffraction and

polarization of electromagnetic radiation proved the

wave nature of radiation.

• Therefore, it is expected that it would explain the

experimental observations made on thermal (heat)

radiation emitted by a blackbody.

Blackbody radiation and Planck hypothesis

• Two patches of clouds in physics sky at the

beginning of 20th century.

• The speed of light Relativity

• The blackbody radiation foundation of

Quantum theory

Blackbody radiation

• Types of heat energy transmission are conduction,

convection and radiation.

• Conduction is transfer of heat energy by molecular

vibrations not by actual motion of material. For example,

if you hold one end of an iron rod and the other end of

the rod is put on a flame, you will feel hot some time

later. You can say that the heat energy reaches your hand

by heat conduction.

• Convection is transfer of heat by actual motion of.

The hot-air furnace, the hot-water heating system,

and the flow of blood in the body are examples.

• Radiation The heat reaching the earth from the

sun cannot be transferred either by conduction or

convection since the space between the earth and

the sun has no material medium. The energy is

carried by electromagnetic waves that do not

require a material medium for propagation. The

kind of heat transfer is called thermal radiation.

• Blackbody is defined as the body which can absorb all

energies that fall on it. It is something like a black hole. No

lights or material can get away from it as long as it is

trapped. A large cavity with a small hole on its wall can be

taken as a blackbody.

•Blackbody radiation: Any radiation that enters the

hole is absorbed in the interior of the cavity, and the

radiation emitted from the hole is called blackbody

radiation.

Fig. 9.1

Blackbody

concave.

3

LAWS OF BLACK BODY RADIATION

1. Stefan and Boltzmann‟s law: it is found that the

radiation energy is proportional to the fourth power of

the associated temperature.

4M (T ) T

M(T) is actually the area under each curve, σ is called

Stefan‟s constant and T is absolute temperature.

2. Wien‟s displacement law: the peak of the curve shifts

towards longer wavelength as the temperature falls and it

satisfies

peakT b

This law is quite useful for measuring the temperature

of a blackbody with a very high temperature. You can

see the example for how to measure the temperature on

the surface of the sun.

where b is called the Wien's constant.

b=2.89X10-3

• The above laws describes the blackbody radiation very

well.

• The problem exists in the relation between the radiation

power Mλ(T) and the wavelength λ.

• Blackbody radiation has nothing to do with both the

material used in the blackbody concave wall and the shape

of the concave wall.

• Two typical theoretical formulas for blackbody

radiation : One is given by Rayleigh and Jeans and the

other by Wein.

3.Rayleigh and Jeans

In 1890, Rayleigh and Jeans obtained a formula using

the classical electromagnetic (Maxwell) theory and the

classical equipartition theorem of energy in thermotics.

The formula is given by

2

3

8 kTE ( )

c

Rayleigh-Jeans formula was correct for very long

wavelength in the far infrared but hopelessly wrong in the

visible light and ultraviolet region. Maxwell‟s

electromagnetic theory and thermodynamics are known as

correct theory. The failure in explaining blackbody

radiation puzzled physicists! It was regarded as ultraviolet

Catastrophe (disaster).

4. Planck Radiation Law:

hcE h

Quantum energy

Planck constant

Frequency

34

15

h 6.626 10 J s

4 .136 10 eV s19

18

1eV 1.602 10 J

1J 6.242 10 eV

4

PLANCK'S QUANTUM HYPOTHESIS —

Energy is quantized

• Max Planck empirical formula explained the

experimental observations.

• In the process of formulation of the formula, he

assumed that the atoms of the walls of the

blackbody behave like small harmonic

oscillators, each having a characteristic

frequency of vibration, lie further made two

radical assumptions about the atomic oscillators.

• (i) An oscillating atom can absorb or mends energy in

discrete units. The indivisible discrete unit of energy hs,

is the smallest amount of energy which can be absorbed

or emitted by the atom and is called an energy quantum.

A quantum of energy has the magnitude given by

E = hv

where v is the frequency of radiation and „h' is a

constant now known as the Planck's constant.

• (ii) The energy of the oscillator is quantized. It can have

only certain discrete amounts of energy En.

En= nhv n=1,2,3……

• The hypothesis that radiant energy is emitted or

absorbed basically in a discontinuous summer and in the

form of quanta is known as the Planck's quantum

hypothesis.

• Planck's hypothesis states that radiant energy Is

quantized and implies that an atom exists in certain

discrete energy states. Such states arc called quantum

stales and n is called the quantum number.

• The atom emits or absorbs energy by jumping from one

quantum state to another quantum state. The

assumption of discrete energy states for an atomic

oscillator (Fig.a) was a departure from the classical

physics and our everyday experience.

• If we take a mass-spring harmonic oscillator, it can

receive any amount of energy form zero to some

maximum value (Fig.b). Thus, in the realm of

classical physics energy always appears to occur with

continuous values and energy exchange between

bodies involves any arbitrary amounts of energy.

PARTICLE PICTURE OF RADIATION —

Radiation is a stream of photons

• Max Planck introduced the concept of discontinuous

emission and absorption of radiation by bodies but he

treated the propagation through space as occurring in the

form of continuous waves as demanded by

electromagnetic theory.

• Einstein refined the Planck's hypothesis and invested the

quantum with a clear and distinct identity.

5

• He successfully explained the experimental results of the

photoelectric effect in 1905 and the temperature

dependence of specific heats of solids in 1907 basing on

Planck's hypothesis.

• The photoelectric effect conclusively established that light

behaves as a swam of particles. Einstein extended

Planck's hypothesis as follows:

1. Einstein assumed that the light energy is not distributed

evenly over the whole expanding wave front but rather

remains concentrated in discrete quanta. He named the

energy quanta as photons. Accordingly, a light beam is

regarded as a stream of photons travelling with a

velocity ' c' .

2. An electromagnetic wave having a frequency f

contains identical photons, each having an energy hƒ.

The higher the frequency of the electromagnetic wave,

the higher is the energy content of each photon.

3. An electromagnetic wave would have energy hƒ if it

contains only one photon. 2hv if it contains 2 photons

and so on. Therefore, the intensity of a

monochromatic light beam I. is related to the

concentration of photons. N. present in the beam.

Thus,

I = N hƒ

Note that according to electromagnetic theory, the

intensity of a light beam is given by

I = 1E12

4. When photons encounter matter, they

impart all their energy to the panicles of

matter and vanish. That is why absorption

of radiation is discontinuous. The number

of photons emitted by even a weak light

source is enormously large and the human

eye cannot register the photons separately

and therefore light appears as a continuous

stream. Thus, the discreteness of light is

not readily apparent.

The Photon

• As the radiant energy is viewed as made up of

spatially localized photons. we may attribute

particle properties to photons. 1. Energy: The energy of a photon is determined by its

frequency v and is given by E = hƒ. Using the relation

ω= 2π and writing h/2π = ħ. we may express E=

ħω

2. Velocity: Photons always travel with the velocity of light

„c'.

3. Rest Mass: The rest mass of photon is zero since a

photon can never be at rest. Thus, m0= 0

4. Relativistic mass: As photon travels with the velocity of

light, it has relativistic mass. given by m= E/c2 = hv/c2

The Photon

• As the radiant energy is viewed as made up of

spatially localized photons. we may attribute

particle properties to photons. 1. Energy: The energy of a photon is determined by its

frequency v and is given by E = hƒ. Using the relation

ω= 2π and writing h/2π = ħ. we may express E= ħω

2. Velocity: Photons always travel with the velocity of light

„c'.

3. Rest Mass: The rest mass of photon is zero since a

photon can never be at rest. Thus, m0= 0

4. Relativistic mass: As photon travels with the velocity of

light, it has relativistic mass. given by m= E/c2 = hv/c2

6

5. Linear Momentum: The linear momentum associated

with a photon may be expressed as p=E/c=hv/c= h/λ

As the wave vector k= 2π/λ , p = hk/ 2π = ħk.

6. Angular Momentum: Angular momentum is also

known as spin which is the intrinsic property of all

microparticles. Photon has a spin of one unit. Thus. s

= lħ.

7. Electrical Charge: Photons are electrically neutral

and cannot be influenced by electric or magnetic

fields. They cannot ionize matter.

Example: Calculate the photon energies for

the following types of electromagnetic

radiation: (a) a 600kHz radio wave; (b) the

500nm (wavelength of) green light; (c) a 0.1

nm (wavelength of) X-rays.

Solution: (a) for the radio wave, we can use the

Planck-Einstein law directly

15 3

9

E h 4.136 10 eV s 600 10 Hz

2.48 10 eV

(b) The light wave is specified by wavelength,

we can use the law explained in wavelength:

6

9

hc 1.241 10 eV mE 2.26eV

550 10 m

(c). For X-rays, we have

6

4

9

hc 1.241 10 eV mE 1.24 10 eV 12.4keV

0.1 10 m

Photoelectric Effect

The quantum nature of light had its origin in the theory

of thermal radiation and was strongly reinforced by the

discovery of the photoelectric effect.

Fig. Apparatus to investigate the photoelectric effect that was

first found in 1887 by Hertz.

Photoelectric Effect

In figure , a glass tube contains two electrodes of the

same material, one of which is irradiated by light. The

electrodes are connected to a battery and a sensitive

current detector measures the current flow between them.

The current flow is a direct measure of the rate of

emission of electrons from the irradiated electrode.

The electrons in the electrodes can be ejected by light

and have a certain amount of kinetic energy. Now we

change:

(1) the frequency and intensity of light,

(2) the electromotive force (e.m.f. or voltage),

(3) the nature of electrode surface.

It is found that:

7

(1). For a given electrode material, no photoemission exists at

all below a certain frequency of the incident light. When the

frequency increases, the emission begins at a certain frequency.

The frequency is called threshold frequency of the material.

The threshold frequency has to be measured in the existence of

e.m.f. (electromotive force) as at such a case the

photoelectrons have no kinetic energy to move from the

cathode to anode . Different electrode material has different

threshold frequency.

(2). The rate of electron emission is directly proportional to

the intensity of the incident light.

Photoelectric current ∝ The intensity of light

(3). Increasing the intensity of the incident light does not

increase the kinetic energy of the photoelectrons.

Intensity of light ∝ kinetic energy of photoelectron

However increasing the frequency of light does increase the

kinetic energy of photoelectrons even for very low intensity

levels.

Frequency of light ∝ kinetic energy of photoelectron

(4). There is no measurable time delay between irradiating

the electrode and the emission of photoelectrons, even

when the light is of very low intensity. As soon as the

electrode is irradiated, photoelectrons are ejected.

(5) The photoelectric current is deeply affected by the nature

of the electrodes and chemical contamination of their

surface.

In 1905, Einstein solved the photoelectric effect

problem by applying the Planck‟s hypothesis. He

pointed out that Planck‟s quantization hypothesis

applied not only to the emission of radiation by a

material object but also to its transmission and its

absorption by another material object. The light is not

only electromagnetic waves but also a quantum. All the

effects of photoelectric emission can be readily

explained from the following assumptions:

(1) The photoemission of an electron from a cathode

occurs when an electron absorbs a photon of the

incident light;

(2) The photon energy is calculated by the Planck‟s

quantum relationship: E = hν.

(3) The minimum energy is required to release an

electron from the surface of the cathode. The

minimum energy is the characteristic of the cathode

material and the nature of its surface. It is called work

function.

Therefore we have the equation of photoelectric effect:

21

2h A mv

Photon energy

Work function

Photoelectron kinetic energy

Using this equation and Einstein‟s assumption, you could

readily explain all the results in the photoelectric effect: why

does threshold frequency exist (problem)? why is the number

of photoelectrons proportional to the light intensity? why does

high intensity not mean high photoelectron energy (problem)?

why is there no time delay (problem)?

8

Example: Ultraviolet light of wavelength 150nm falls on

a chromium electrode. Calculate the maximum kinetic

energy and the corresponding velocity of the

photoelectrons (the work function of chromium is

4.37eV).

Solution: using the equation of the photoelectric effect, it

is convenient to express the energy in electron volts. The

photon energy is6

9

1.241 108.27

150 10

hc eV mE h eV

mand2

2

1

2

1(8.27 4.37) 3.90

2

h A mv

mv eV eV

19 19 19 2 21 1.602 10 1.602 10 1.602 10eV J N m kg m s

∴2 19 2 21

3.90 3.90 1.602 102mv eV kg m s

∴19

6

31

2 3.90 12.496 101.17 10 /

9.11 10

eVv m s

m

Examples

1. The wavelength of yellow light is 5890 A. What

is the energy of the photons in the beam?

Empress in electron volts.

2. 77w light sensitive compound on most

photographic films is silver bromide, Aglin A

film is exposed when the light energy absorbed

dissociates this molecule into its atoms. The

energy of dissociation of Agllr is 23.9 k.catitnot

Find the energy in electron volts, the wavelength

and the frequency of the photon that is just able

to dissociate a molecule of silver bromide.

3. Calculate the energy of a photon of blue light with a

frequency of 6.67 x 1014 Hz. (State in eV) [2.76eV]

4. Calculate the energy of a photon of red light with a

wavelength of 630 nm. [1.97eV]

5. Barium has a work function of 2.48 eV. What is the

maximum kinetic energy of the ejected electron if the

metal is illuminated by light of wavelength 450 nm?

[0.28 eV]

6. When a 350nm light ray falls on a metal, the maximum

kinetic energy of the photoelectron is 1.20eV. What is the

work function of the metal? [2.3 eV]

7. A photon has 3.3 x 10-19 J of energy. What is the

wavelength of this photon?

8. What is the energy of one quantum of 5.0 x 1014 Hz light?

6/18/2014

1

X - Rays

Objectives

• Introduction and production of X-Rays

• Properties of X-Rays

• Diffraction of X-Rays

• The Bragg’s X-Ray spectrometer

• Continuous spectra

• Characteristics Radiation

• Moseley’s law

• Absorption of X-Ray

• Compton effect

• Applications of X-Rays

Introduction of X-Rays• Rontgen discovered X-rays in 1985 during some

experiments with a discharge tube.

• He noticed that a screen coated with bariumplatinocyanide present at a distance from the dischargetube. Rontgen called these invisible radiations “X-rays”.

Finally, he concluded that X-rays are produced dueto the bombardment of cathode rays on the walls of thedischarge tube.

• X-rays are highly penetrating and it can pass throughmany solids.

• X-rays occur beyond the UV region in theelectromagnetic spectrum.

• Their wavelengths range from 0.01 to 10 Å.

Production or Generation of X-raysX-rays are produced by an X-ray tube. The

schematic of the modern type of X-ray tube isshown in above figure.

It is an evacuated glass bulb enclosing twoelectrodes, a cathode and an anode.

The cathode consists of a tungsten filament whichemits electrons when it heated. The electrons arefocused into a narrow beam with the help of ametal cup S.

The anode consists of a target material, made oftungsten or molybdenum, which is embedded in acopper bar.

Water circulating through a jacket surroundingthe anode and cools the anode. Further largecooling fins conduct the heat away to theatmosphere.

• The face of the target is kept at an anglerelative to the oncoming electron beam. A veryhigh potential difference of the order of 50 kV isapplied across the electrodes.

The electrons emitted by the cathode areaccelerated by the anode and acquire highenergies of order of 105 eV. When the targetsuddenly stops these electrons, X-rays are emitted.

• The magnetic field associated with the electronbeam undergoes a change when the electrons arestopped and electromagnetic waves in the form ofX-rays are generated.

6/18/2014

2

• The grater of the speed of the electron beam, theshorter will be the wavelength of the radiated X-rays.Only about 0.2 % of the electron beam energy isconverted in to X-rays and the rest of the energytransforms into heat. It is for the reason that theanode is intensively cooled during the operation ofX-ray tube.

• The intensity of the electron beam depends on thenumber of electron leaving the cathode. The hardnessof the X-rays emitted depends on the energy of theelectron beam striking the target. It can be adjustedby varying the potential difference applied betweenthe cathode and anode. Therefore, the largerpotential difference, the more penetrating or harderX-rays.

Properties of X-Rays…

They have relatively high penetrating power.

They are classified into Hard X-rays & Soft X-rays.

The X-rays which have high energy and shortwavelength is known as Hard X-rays.

The X-rays which have low energy andlonger wavelength is known as Soft X-rays.

X-rays causes the phenomenon of flouroscence.

On passing through a gas X-rays ionize the gas.

Properties of X-Rays…

They are absorbed by the materials throughwhich they traverse.

X-rays travel in straight line. Their speed invacuum is equal to speed of light .

X-rays can affect a photographic film.

X-rays are undeflected by electric field ormagnetic field.

Diffraction of X-Rays – Bragg’s law

Consider a crystal as made out ofparallel planes of ions, spaced a distance dapart. The conditions for a sharp peak in theintensity of the scattered radiation are:

1. That the X-rays should be secularly reflectedby the ions in any one plane.

2. That the reflected rays from successiveplanes should interfere constructively.

• Path difference between two rays reflectedfrom adjoining planes: 2dsinθ,

• For the rays to interfere constructively,this path difference must be an integralnumber of wavelength λ,

nλ =2dsinθ ------- (1)

Bragg angle is just the half of the total angle by which the incident beam is deflected.

The Bragg’s X-Ray spectrometer• An X-ray diffraction experiment requires,

• X-ray source

• The sample

• The detector

• Depending on method there can be variations inthese requirements. The X-ray radiation mayeither monochromatic or may have variablewave length.

• Structures of polycrystalline sample and singlecrystals can be studied. The detectors used inthese experiments are photographic film.

6/18/2014

3

The schematic diagram of Bragg’s X-rayspectrometer is given in above.

• X-ray from an X-ray tube is collimated by passing teamthrough slits S1 and S2. This beam is then allowed tofall on a single crystal mounted on a table which canbe rotated about an axis perpendicular to the plane ofincident of X-rays. The crystal behaves as a reflectedgrating and reflects X-rays. By rotating the table, theglancing angle θ at which the X-ray is incident on thecrystal can be changed. The angle for which theintensity of the reflected beam is maximum gives thevalue of θ. The experiment is repeated for each planeof the crystal. For first order reflection n = 1 so that, λ= 2d sinθ; for n = 2, 2λ = 2d sinθ; ……., and so on.

• A photographic plate or an ionization chamber isused to detect the rays reflected by the crystal.

Continuous or Bremsstrahlung X-rays

• "Bremsstrahlung" means "braking radiation" and

is retained from the original German to describe

the radiation which is emitted when electrons are

decelerated or "braked" when they are fired at a

metal target.

• Accelerated charges give off electromagneticradiation, and when the energy of thebombarding electrons is high enough, thatradiation is in the x-ray region ofthe electromagnetic spectrum.

Continuous X-rays…

Continuous X-rays…• It is characterized by a continuous distribution of

radiation which becomes more intense andshifts toward higher frequencies when theenergy of the bombarding electrons is increased.

• The curves above are who bombarded tungstentargets with electrons of four different energies.

• The continuous distribution of x-rays whichforms the base for the two sharp peaks at left iscalled "Bremsstrahlung" radiation.

Characteristic X-rays• Characteristic X-rays are emitted from heavy

elements when their electrons make transitionsbetween the lower atomic energy levels.

http://hyperphysics.phy-astr.gsu.edu/hbase/ems3.html






http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/xrayc.html



6/18/2014

4

Characteristic X-rays…

• Characteristic X-rays emission which shown as twosharp peaks in the illustration at left occur whenvacancies are produced in the n = 1 or K-shell ofthe atom and electrons drop down from above tofill the gap.

• The X-rays produced by transitions from the n = 2to n = 1 levels are called Kα X-rays, and those forthe n = 3->1 transition are called Kβ X-rays.

• Transitions to the n=2 or L-shell are designated asL - shall X-rays (n= 3->2 is Lα, n = 4->2 is Lβ, etc.

Uses of Characteristic X-rays..

• Characteristic X-rays are used for theinvestigation of crystal structure by X-raydiffraction.

• Crystal lattice dimensions may be determinedwith the use of Bragg's law in a Braggspectrometer.

Moseley’s law and its importance.• The English physicist Henry Moseley (1887-1915)

found, by bombarding high speed electrons on ametallic anode, that the frequencies of theemitted X-ray spectra were characteristic of thematerial of the anode.

• The spectra were called characteristic X-rays.

• He interpreted the results with the aid of the Bohrtheory, and found that the wavelengths λ of theX-rays were related to the electric charge Z of thenucleus. According to him, there was thefollowing relation between the two values(Moseley’s law; 1912).

1/λ = c(Z - s)2

Where,

c and s are constants applicable to all elements

Z is an integer.

When elements are arranged in lineaccording to their position in the Periodic Table ,the Z value of each element increases one byone.

Moseley correctly interpreted that the Zvalues corresponded to the charge possessed bythe nuclei. Z is none other than the atomicnumber.

It was found that the characteristic X-ray of an unknownelement was 0.14299 x 10-9 m. Thewavelength of the same series of the characteristic X-rayof a known element Ir (Z = 77) is 0.13485x 10-9 m. Assuming s = 7.4, estimate the atomic number ofthe unknown element.

Importance of Moseley’s law

• Atomic no. is more important than Atomicweight as it is equals to charge of nucleus.

• Difference between Ni, Co, Te & I etc., isexplained when periodic table was constructedwith atomic no.

• Moseley predicted the existence of elementswith atomic no. 43, 61, 72 & 75. Thus, X-rayspectrum analysis new elements can bediscovered.

6/18/2014

5

Absorption of X-RayWhen the X-rays hit a sample, the oscillating

electric field of the electromagnetic radiationinteracts with the electrons bound in an atom.

A narrow parallel monochromatic x-ray beam ofintensity I0 passing through a sample of thickness x willget a reduced intensity I according to the expression:

ln (I0 /I) = μ x ------- (1)

Where μ is the linear absorption coefficient,which depends on the types of atoms and the densityρ of the material.

At certain energies where the absorptionincreases drastically and gives rise to an absorptionedge. Each such edge occurs when the energy of theincident photons is just sufficient to cause excitationof a core electron of the absorbing atom to acontinuum state, i.e. to produce a photoelectron.

The absorption edges are labeled in the orderof increasing energy, K, LI, LII, LIII, MI,….,corresponding to the excitation of an electron fromthe 1s(2S½), 2s(2S½), 2p(2P½), 2p(2P3/2), 3s(2S½), …orbitals (states), respectively.

Thus, the energies of theabsorbed radiation atthese edges correspondto the binding energiesof electrons in the K, L,M, etc.., shells of theabsorbing elements.

Compton effect

A phenomenon called Compton scattering,first observed in 1924 by Compton, and providesadditional direct confirmation of the quantumnature of electromagnetic radiation. When X-raysimpinges on matter, some of the radiation isscattered, just as the visible light falling on arough surface undergoes diffuse reflection.

• Observation shows that some of the scatteredradiation has smaller frequency and longerwavelength than the incident radiation, andthat the change in wavelength depends on theangle through which the radiation is scattered.

• Specifically, if the scattered radiation emergesat an angle φ with the respect to the incidentdirection, and if f and i are the wavelength ofthe incident and scattered radiation,respectively, it is found that, Where, m0 is the electron mass.

6/18/2014

6

• In figure, the electron is initially at restwith incident photon of wavelength andmomentum p; scattered photon with longerwavelength f and momentum p and recoilingelectron with momentum P. The direction ofthe scattered photon makes an angle φ withthat of the incident photon, and the anglebetween p and p is also φ.

called Compton wavelength.

nmmc

hc

00243.0

• Compton scattering cannot be understoodon the basis classical electromagnetic theory.

• On the basis of classical principles, thescattering mechanism is induced by motionof electrons in the material, caused by theincident radiation.

Applications of X-Rays…X-rays are used in industrial, medical, pure

science research and X-ray crystallography etc…

• X-rays are used to detect defects in radio valves.

• X-rays are used to detect cracks in structures.

• X-rays are used to analyses the structures ofalloys and other composite bodies by diffractionof X-rays.

• They are also used to study are structure ofmaterials like rubber, cellulose, plastic, fibres etc…

• X-rays can destroy abnormal internal tissues.

Applications of X-Rays…• X-rays are used in analysis of crystal structure and

structure of complex organic molecule.

• They are also used in determining the atomicnumber and identification of various chemicalelements.

• X-rays are used to detect fractures and formationof stones in human body.

• They are also being used for tumor treatment andfor this purpose hard X-rays are used.

• X-rays are also used in X-ray crystallography forLaue method, Rotating crystal method, Powdermethod, etc….

6/18/2014

1

When matter

vibrates or moves

back and forth

very quickly,

sound is

produced.

Example: When

you hit a drum,

parts of the drum

will vibrate

creating sound.

•The sound that

Produce pleasing

effect on the ear is

called Musical sound.

•Musical instruments

make different sounds

by plucking the

strings.

•Example:-sound

produce by instrument

sitar,violin,flute,piano

etc

•The sound that

Produce Jarring effect

on the ear is called

Noise sound.

•Noice sound make

unpleasent to hear

•Example:-sound

produce by flying

aeroplane,road

traffic,cracker etc

6/18/2014

2

6/18/2014

3

Loudness is directly proportional to the logaritham of

intensity and that is known as weber fechner law.

Loudnessness is a degree of sensation produce on

ear.thus loudness various from one listner to another."

Loudness depends upon intensity and also upon the

sensitiveness of the ear.

Thus “loudness is characteristic which is common to

all sounds whether classified as musical or noise

sound.

Amount of sound energy

not reflected

a= sound energy

absorbed/sound energy

incident

Unit of „a‟ sabine also

called OWU

16

Sound Absorption

The property of a surface by which sound energy is converted into other form of energy is known as absorption.

In the process of absorption sound energy is converted into heat due to frictional resistance inside the pores of the material.

The fibrous and porous materials absorb sound energy more, than other solid materials.

17

Sound Absorption Coefficient

The effectiveness of a surface in absorbing

sound energy is expressed with the help of

absorption coefficient.

The coefficient of absorption ` ‟ of a materials

is defined as the ratio of sound energy absorbed

by its surface to that of the total sound energy

incident on the surface.

surfacetheonincidentenergysoundTotal

surfacethebyabsorbedenergySound=

18

A unit area of open window is selected as the

standard. All the sound incident on an open

window is fully transmitted and none is

reflected. Therefore, it is considered as an

ideal absorber of sound.

Thus the unit of absorption is the open

window unit (O.W.U.), which is named a

“sabin” after the scientist who established the

unit.

A 1m2 sabin is the amount of sound absorbed

by one square metre area of fully open

window.

6/18/2014

4

19

The value of ` ‟ depends on the nature of the

material as well as the frequency of sound. It is

a common practice to use the value of ` ‟ at

500 Hz in acoustic designs.

If a material has the value of “ ” as 0.5, it

means that 50% of the incident sound energy

will be absorbed per unit area.

If the material has a surface area of S sq.m.,

then the absorption provided by that material

is

a = . S

20

If there are different materials in a hall, then the

total sound absorption by the different

materials is given by

A = a1 + a2 + a3 + ……

A = 1S1 + 2S2 + 3S3 + ……

or A =

where 1, 2, 3 ………. are absorption

coefficients of materials with areas S1, S2, S3,

…….

n

nnS

1

21

Reverberation

Sound produced in an enclosure does not die

out immediately after the source has ceased to

produce it.

A sound produced in a hall undergoes multiple

reflections from the walls, floor and ceiling

before it becomes inaudible.

A person in the hall continues to receive

successive reflections of progressively

diminishing intensity.

This prolongation of sound before it decays to

a negligible intensity is called reverberation.

22

Reverberation Time

The time taken by the sound in a room to fall

from its average intensity to inaudibility level is

called the reverberation time of the room.

Reverberation time is defined as the time

during which the sound energy density falls

from its steady state value to its one-millionth

(10-6) value after the source is shut off.

23

If initial sound level is Li and the final level is Lf

and reference intensity value is I ,then we

can write

Li = 10 log and Lf = 10 log

Li – Lf = 10 log

As = 10-6,

Li – Lf = 10 log 106 = 60 dB

Thus, the reverberation time is the period of

time in seconds, which is required for sound

energy to diminish by 60 dB after the sound

source is stopped.

I

Ii

I

If

f

i

I

I

i

f

I

I

24

Sabine’s Formula for Reverberation Time

Prof.Wallace C.Sabine (1868-1919) determined the reverberation times of empty halls and furnished halls of different sizes and arrived at the following conclusions.

The reverberation time depends on the reflecting properties of the walls, floor and ceiling of the hall.

The reverberation time depends directly upon the physical volume V of the hall.

The reverberation time depends on the absorption coefficient of various surfaces such as carpets, cushions, curtains etc present in the hall.

The reverberation time depends on the frequency of the sound wave because absorption coefficient of most of the materials increases with frequency.

6/18/2014

5

25

Prof. Sabine summarized his results in the form of the following equation.

Reverberation Time, T

or

T =

where K is a proportionality constant.

It is found to have a value of 0.161 when the dimensions are measured in metric units. Thus,

T =

This Equation is known as Sabine’s formula for reverberation time.

A

VK

A

V161.0

AAbsorption

VHalltheofVolume

,

,

26

It may be rewritten as

T =

or T =

N

nnS

V

1

161.0

nnSSSS

V

.......

161.0

332211

27

Factors Affecting Acoustics of Buildings

(1) Reverberation Time

• If a hall is to be acoustically satisfactory, it is

essential that it should have the right reverberation

time.

• The reverberation time should be neither too long

nor too short.

• A very short reverberation time makes a room

`dead’. On the other hand, a long reverberation time

renders speech unintelligible.

• The optimum value for reverberation time depends

on the purpose for which a hall is designed. 28

Remedies

The reverberation time can be controlled by the

suitable choice of building materials and furnishing

materials.

Since open windows allow the sound energy to

flow out of the hall, there should be a limited

number of windows. They may be opened or

closed to obtain optimum reverberation time.

29

(2) Loudness

Sufficient loudness at every point in the hall is an

important factor for satisfactory hearing.

Excessive absorption in the hall or lack of reflecting

surfaces near the sound source may lead to decrease

in the loudness of the sound.

Remedies

A hard reflecting surface positioned near the sound

source improve the loudness.

Low ceilings are also of help in reflecting the sound

energy towards the audience.

Adjusting the absorptive material in the hall will

improve the situation.30

(3) Focussing

Reflecting concave surfaces cause concentration of reflected sound, creating a sound of larger intensity at the focal point. These spots are known as sound foci.

Such concentrations of sound intensity at some points lead to deficiency of reflected sound at other points.

The spots of sound deficiency are known as dead spots. The sound intensity will be low at dead spots and inadequate hearing.

Further, if there are highly reflecting parallel surfaces in the hall, the reflected and direct sound waves may form standing waves which leads to uneven distribution of sound in the hall.

6/18/2014

6

31

Remedies

The sound foci and dead spots may be eliminated if curvilinear interiors are avoided. If such surfaces are present, they should be covered by highly absorptive materials.

Suitable sound diffusers are to be installed in the hall to cause even distribution of sound in the hall.

A paraboloidal reflecting surface arranged with the speaker at its focus is helpful in directing a uniform reflected beam of sound in the hall.

32

(4) Echoes

When the walls of the hall are parallel, hard and separated by about 34m distance, echoes are formed. Curved smooth surfaces of walls also produce echoes.

Remedies

This defect is avoided by selecting proper shape for the auditorium. Use of splayed side walls instead of parallel walls greatly reduces the problem and enhance the acoustical quality of the hall.

Echoes may be avoided by covering the opposite walls and high ceiling with absorptive material.

33

(5) Echelon effect

If a hall has a flight of steps, with equal width, the sound waves reflected from them will consist of echoes with regular phase difference. These echoes combine to produce a musical note which will be heard along with the direct sound. This is called echelon effect. It makes the original sound unintelligible or confusing.

Remedies

It may be remedied by having steps of unequal width.

The steps may be covered with proper sound absorbing materials, for example with a carpet.

34

(6) Resonance

Sound waves are capable of setting physical

vibration in surrounding objects, such as window

panes, walls, enclosed air etc. The vibrating

objects in turn produce sound waves. The

frequency of the forced vibration may match some

frequency of the sound produced and hence result

in resonance phenomenon. Due to the resonance,

certain tones of the original music may get

reinforced that may result in distortion of the

original sound.

Remedies

The vibrations of bodies may be suitably damped

to eliminate resonance due to them by proper

aintenance and selection.

35

(7) Noise

Noise is unwanted sound which masks the

satisfactory hearing of speech and music.

There are mainly three types of noises that are to

be minimized.

They are (i) air-borne noise,

(ii) structure-borne noise and

(iii) internal noise.

36

The noise that comes into building through air

from distant sources is called air-borne noise.

A part of it directly enters the hall through the

open windows, doors or other openings while

another part enters by transmission through walls

and floors.

Remedies

The building may be located on quite sites away

from heavy traffic, market places, railway

stations, airports etc.

They may be shaded from noise by interposing a

buffer zone of trees, gardens etc.

(i) Air-Borne Noise

6/18/2014

7

37

The noise which comes from impact sources on

the structural extents of the building is known- as

the structure-borne noise. It is directly transmitted

to the building by vibrations in the structure. The

common sources of this type of noise are foot-

steps, moving of furniture, operating machinery

etc.

Remedies

The problem due to machinery and domestic

appliances can be overcome by placing vibration

isolators between machines and their supports.

Cavity walls, compound walls may be used to

increase the noise transmission loss.

(ii) Structure-Borne Noise

38

Internal noise is the noise produced in the hall or

office etc.

They are produced by air conditioners,

movement of people etc.

Remedies

The walls, floors and ceilings may be provided

with enough sound absorbing materials.

The gadgets or machinery should be placed on

sound absorbent material.

(iii) Internal Noise

http://www.studyyaar.com/index.php/module-

video/watch/303-acoustics-basic-concepts

srmuniv.ac.in/openware_d_loads/u1L-7.ppt

www.umiacs.umd.edu/~ramani/cmsc828d_audio/828d_l2

0.pdf

1 Engineering Physics by H Aruldhas, PHI India

2 Engineering Physics by B K Pandey , S. Chaturvedi,

Cengage Learning

Resnick, Halliday and Krane, Physics part I and II, 5th

Edition John Wiely

Engineering Physics by S.CHAND

Engineering Physics by G VIJIYAKUMARI

Engineering Physics by Tech max publication

http://www.studyyaar.com/index.php/module-video/watch/303-acoustics-basic-concepts









http://www.umiacs.umd.edu/~ramani/cmsc828d_audio/828d_l20.pdf

http://www.umiacs.umd.edu/~ramani/cmsc828d_audio/828d_l20.pdf

6/18/2014

1

ULTRASONIC WAVES

1

Topic cover through ultrasonic are….

Introduction to Ultrasonics

Properties of Ultrasonic waves

Ultrasonic Production- Magnetostriction

Method

Ultrasonic Production- Piezo Electric Method

Applications of Ultrasonics

Worked Problem

2

Introduction to Ultrasonics

The word ultrasonic combines the Latin rootsultra, meaning ‘beyond’ and sonic, or sound.

The sound waves having frequencies above theaudible range i.e. above 20000Hz are calledultrasonic waves.

Generally these waves are called as highfrequency waves.

The field of ultrasonics have applications forimaging, detection and navigation.

The broad sectors of society that regularly applyultrasonic technology are the medicalcommunity, industry, the military and privatecitizens.

3

Properties of ultrasonic waves

(1) They have a high energy content.

(2) Just like ordinary sound waves, ultrasonic waves

get reflected, refracted and absorbed.

(3) They can be transmitted over large distances

with no appreciable loss of energy.

(4) If an arrangement is made to form stationary waves of ultrasonic in a liquid, it serves as a diffraction grating. It is called an acoustic grating.

(5) They produce intense heating effect when passed through a substance.

4

Ultrasonics Production

Ultrasonic waves are produced by the

following methods.

(1) Magnetostriction generator or oscillator

(2) Piezo-electric generator or oscillator

5

Magnetostriction Generator

Principle: Magnetostriction effect

When a ferromagnetic rod like iron or nickel isplaced in a magnetic field parallel to its length,the rod experiences a small change in its length.This is called magnetostriction effect.

6

6/18/2014

2

7

The change in length (increase or decrease) produced

in the rod depends upon the strength of the magnetic

field, the nature of the materials and is independent of

the direction of the magnetic field applied.

Construction

The experimental arrangement is shown in Figure

Magnetostriction oscillator8

XY is a rod of ferromagnetic materials like iron ornickel. The rod is clamped in the middle.

The alternating magnetic field is generated byelectronic oscillator.

The coil L1 wound on the right hand portion of therod along with a variable capacitor C.

This forms the resonant circuit of the collectortuned oscillator. The frequency of oscillator iscontrolled by the variable capacitor.

The coil L2 wound on the left hand portion of the rod is connected to the base circuit. The coil L2acts as feed –back loop.

9

Working

When High Tension (H.T) battery is switched on,the collector circuit oscillates with a frequency,

f =

This alternating current flowing through the coilL1 produces an alternating magnetic field alongthe length of the rod. The result is that the rodstarts vibrating due to magnetostrictive effect.

10

1

1

2 L C

The frequency of vibration of the rod is given by

n =

where l = length of the rod

Y = Young’s modulus of the rod material and

=density of rod material

Y

l2

1

11

•The capacitor C is adjusted so that the frequency of

the oscillatory circuit is equal to natural frequency of

the rod and thus resonance takes plate.

•Now the rod vibrates longitudinally with maximum

amplitude and generates ultrasonic waves of high

frequency from its ends.

Advantages

1. The design of this oscillator is very simple and its

production cost is low

2. At low ultrasonic frequencies, the large power

output can be produced without the risk of damage

of the oscillatory circuit.

12

Disadvantages

1. It has low upper frequency limit and cannot

generate ultrasonic frequency above 3000 kHz (ie.

3MHz).

2. The frequency of oscillations depends on

temperature.

3. There will be losses of energy due to hysteresis

and eddy current.

6/18/2014

3

Piezo Electric Generator or Oscillator

Principle : Inverse piezo electric effect

If mechanical pressure is applied to one pair ofopposite faces of certain crystals like quartz, equaland opposite electrical charges appear across itsother faces. This is called as piezo-electric effect.

The converse of piezo electric effect is also true.

If an electric field is applied to one pair of faces,the corresponding changes in the dimensions ofthe other pair of faces of the crystal are produced.This is known as inverse piezo electric effect orelectrostriction.

13

Construction

The circuit diagram is shown in Figure

Piezo electric oscillator

14

The quartz crystal is placed between two metalplates A and B.

The plates are connected to the primary (L3) of atransformer which is inductively coupled to theelectronics oscillator.

The electronic oscillator circuit is a base tunedoscillator circuit.

The coils L1 and L2 of oscillator circuit aretaken from the secondary of a transformer T.

The collector coil L2 is inductively coupled tobase coil L1.

The coil L1 and variable capacitor C1 form the tank circuit of the oscillator.

15

Working

When H.T. battery is switched on, the oscillator produces highfrequency alternating voltages with a frequency.

Due to the transformer action, an oscillatory e.m.f. is induced in thecoil L3. This high frequency alternating voltages are fed on the plates Aand B.

Inverse piezo-electric effect takes place and the crystal contractsand expands alternatively.The crystal is set into mechanicalvibrations.

The frequency of the vibration is given by

n =

112

1

CLf

Y

l

P

2

16

where P = 1,2,3,4 … etc. for fundamental,

first over tone, second over tone etc.,

Y = Young’s modulus of the crystal and

ρ = density of the crystal.

The variable condenser C1 is adjusted such that

the frequency of the applied AC voltage is equal

to the natural frequency of the quartz crystal,

and thus resonance takes place.

The vibrating crystal produces longitudinal

ultrasonic waves of large amplitude.

17

Advantages

Ultrasonic frequencies as high as 5 x 108Hz or

500 MHz can be obtained with this arrangement.

The output of this oscillator is very high.

It is not affected by temperature and humidity.

Disadvantages

The cost of piezo electric quartz is very high

The cutting and shaping of quartz crystal are

very complex.

18

6/18/2014

4

Detection of Ultrasonic Waves

1. Piezoelectric Detector

Piezoelectric effect can also be used to detect ultrasonics. If

ultrasonics comprising of compressions and rarefactions are

allowed to fall upon a quartz crystal a certain potential

difference is developed across the faces which after

amplification by a value amplifier can be used to detect

ultrasonics.

2. Kundt’s Tube Method

Kundt’s tube is a long glass tube supported horizontally

with a air column in it when the ultrasonic waves are passed

the Kundt’s tube, the lycopodium powder sprinkled in the

tube collects in the form of heaps at the nodal points and is

blown off at the antinodal points. This method is used

provided that the wavelength is not very small.

19

3 Thermal Detector

This is the most commonly used method of

detection of ultrasonic waves. In this method, a fine

platinum wire is used. This wire is moved through

the medium.

At the position of nodes, due

to alternate compressions ad rarefactions, adiabatic

changes in temperature takes place. The resistance

of the platinum wire changes with respect to time.

This can be detected with the help of Callendar and

Garrifith’s bridge arrangement.

At the position of the antinodes, the temperature

remains constant. This will be indicated by the

undisturbed balanced position of the bridge.

20

4. flame Method

A narrow sensitive flame is moved along

the medium. At the positions of antinodes, the flame

is steady.

At thepositions of nodes, the flame flickers because

there is a change in pressure. In this way, positions

of nodes and antinodes can be found out in

the medium. The average distance between the two

adjacent nodes is equal to half the wavelength.

If the value of the frequency of ultrasonic wave is

known, the velocity of ultrasonic wave propagated

through the medium can be calculated.

21

Acoustic Diffraction Method

(Determination of the velocity)

This method is based on the fact that ultrasonic

waves which consist of alternate compressions

and rarefactions changes the density of the

medium through which they pass.

This leads to a periodic variation of refractive

index of the liquid, such a liquid column is

subjected to ultrasonic waves constitutes an

acoustical grating. If monochromatic light is

passed through the waves the liquid causes the

diffraction of light.

22

Figure shows the experimental arrangement,

standing ultrasonic waves are produced in a

liquid contained in a glass tube. The density and so

the refractive index of the liquid is maximum at

the nodal point and minimum at antinodal points.

Hence the nodal area acts as opaque region, while

antinodal area acts as transparent region for light.

The liquid column thus resembles the rules grating.

23 24

The grating period d equal to /λ/2 and is given by

d sine θ=mλ

Where

λ= wavelength of monochromatic light beam

m = order of minima.

An acoustic diffraction grating produced by a liquid

column subjected to ultrasonic waves

6/18/2014

5

(1)Detection of flaws in metals(NDT)

Principle

Ultrasonic waves are used to detect the presence

of flaws or defects in the form of cracks,

blowholes porosity etc., in the internal structure

of a material

By sending out ultrasonic beam and by

measuring the time interval of the reflected

beam, flaws in the metal block can be

determined.

25

Applications of Ultrasonic Waves in Engineering

Experimental setup

It consists of an ultrasonic frequency generator and

a cathode ray oscilloscope (CRO),transmitting

transducer(A), receiving transducer(B) and an

amplifier.

26

Working

In flaws, there is a change of medium and this

produces reflection of ultrasonic at the cavities or

cracks.

The reflected beam (echoes) is recorded by using

cathode ray oscilloscope.

The time interval between initial and flaw echoes

depends on the range of flaw.

By examining echoes on CRO, flaws can be

detected and their sizes can be estimated.

27

(2) Ultrasonic Drilling

Ultrasonics are used for making holes invery hard materials like glass, diamondetc.

For this purpose, a suitable drilling toolbit is fixed at the end of a powerfulultrasonic generator.

Some slurry (a thin paste of carborundumpowder and water) is made to flowbetween the bit and the plate in which thehole is to be made

Ultrasonic generator causes the tool bit tomove up and down very quickly and theslurry particles below the bit just removesome material from the plate.

This process continues and a hole isdrilled in the plate.

28

(3) Ultrasonic welding

The properties of some metals change onheating and therefore, such metals cannot bewelded by electric or gas welding.

In such cases,the metallic sheets are weldedtogether at room temperature by usingultrasonic waves.

29

(4) Ultrasonic soldering

Metals like aluminium cannot be directlysoldered.However, it is possible to solder suchmetals by ultrasonic waves.

An ultrasonic soldering iron consists of anultrasonic generator having a tip fixed at its endwhich can be heated by an electrical heatingelement.

The tip of the soldering iron melts solder on thealuminium and the ultrasonic vibrator removesthe aluminium oxide layer.

The solder thus gets fastened to clear metalwithout any difficulty.

30

6/18/2014

6

(5) Ultrasonic cutting and machining

Ultrasonic waves are used for cutting and machining.

31

(6) Ultrasonic cleaning

It is the most cheap technique employed for

cleaning various parts of the machine, electronic

assembles, armatures, watches etc., which

cannot be easily cleaned by other methods.

(7) SONAR

SONAR is a technique which stands for SoundNavigation and Ranging.

It uses ultrasonics for the detection and identificationof under water objects.

The method consists of sending a powerful beam ofultrasonics in the suspected direction in water.

By noting the time interval between the emission andreceipt of beam after reflection, the distance of theobject can be easily calculated.

The change in frequency of the echo signal due to theDopper effect helps to determine the velocity of thebody and its direction.

32

Measuring the time interval (t) between the transmitted

pulses and the received pulse,

the distance between the transmitter and the remote

object is determined using the formula., where v is the

velocity of sound in sea water.

The same principle is used to find the depth of the sea.

2

tvd

33

1. Sonar is used in the location of shipwrecks and

submarines on the bottom of the sea.

2. It is used for fish-finding application .

3. It is used for seismic survey.

Applications of SONAR

Applications of Ultrasonics in Medicine

(1)Diagnostic sonography

Medical sonography (ultrasonography) is an ultrasound-based diagnostic medical imaging technique used tovisualize muscles, tendons, and many internal organs,their size, structure and any pathological lesions.

34

Obstetric ultrasound is primarily used to:

•Date the pregnancy

•Check the location of the placenta

•Check for the number of fetuses

•Check for physical abnormities

•Check the sex of the baby

•Check for fetal movement, breathing, and

heartbeat.

(2)Ultrasound therapeutic applications

• More power ultrasound sources may be usedto clean teeth in dental hygiene or generatelocal heating in biological tissue, e.g. inoccupational therapy, physical therapy andcancer treatment.

• Extracorporeal shock wave lithotripsy uses apowerful focused ultrasound source to breakup kidney stones.

• We can also use it in Ultrasonic bloodFlow meter

35

Ultrasound in research

Scientists often use in research, for instant to breakup high molecular weight polymers, thus creatingnew plastic materials.

Indeed, ultrasound also makes it possible todetermine the molecular weight of liquidpolymers, and to conduct other forms ofinvestigation on the physical properties ofmaterials.

Ultrasonic can also speed up certain chemicalreactions. Hence it has gained application inagriculture, that seeds subjected to ultrasound maygerminate more rapidly and produce higher yields.

36

6/18/2014

7

Worked Problem

A quartz crystal of thickness 1 mm is vibrating

at resonance. Calculate the fundamental

frequency. Given Y for quartz = 7.9 x 1010

Nm-2 and ρ for quartz = 2650 kg m-3.

37

Here P = 1

f =

= 2.72998 x 106 Hz

The fundamental frequency of the quartz crystal

= 2.730 x 106 Hz = 2.73MHz

2650

109.7

001.02

110

38

STUDENTS YOU CAN ALSO REFER THE SITE..

http://www.vidyarthiplus.in

http://www.slideshare.net/rencyfrancis/ultrasonics

http://www.newagepublishers.com/samplechapter/00

1649.pdf

1 Engineering Physics by H Aruldhas, PHI India

2 Engineering Physics by B K Pandey , S.

Chaturvedi, Cengage Learning

Resnick, Halliday and Krane, Physics part I and II,

5th Edition John Wiely

Engineering Physics by S.CHAND

Engineering Physics by G VIJIYAKUMARI 39

http://www.vidyarthiplus.in/

http://www.slideshare.net/rencyfrancis/ultrasonics



Ep pp ts

Education

Transcript of Ep pp ts