Optics - Trinity College, Dublin · Geometrical Optics-subset of optics concerning interaction of...

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Geometrical Optics Reflection Refraction Critical angle Total internal reflection Lecture 16: Polarisation of light waves

Transcript of Optics - Trinity College, Dublin · Geometrical Optics-subset of optics concerning interaction of...

Geometrical Optics

• Reflection

• Refraction

• Critical angle

• Total internal reflection

Lecture 16:

Polarisation of light waves

Geometrical Optics- subset of optics concerning

interaction of light with macroscopic material

Geometrical Optics

Optics—Branch of Physics,

concerning the interaction of light with matter

Dimension larger than a human hair ≈ 50mm

Light can travel through

•empty space,

•air, glass, water,

•cornea,

•eye lens etc.

each one referred to as a medium

Geometrical Optics ray optics

Light Ray –beam of light

Light rays will travel in a straight line if they

remain in the same medium

At the boundary between two media, the light

ray can change direction by

Reflection or Refraction

Reflection

For a mirror (smooth metal surface)

“all” light will be reflected

Reflection

Normal

Incident Ray Reflected Ray

qi qr

Smooth

Metal surface

Rough Surface

No unique angle of reflection for all rays

Light reflected in all directions

Diffuse reflection

Reflection

Majority of objects (clothing, plants, people, etc)

are visible because they reflect light in

a diffuse manner.

Normal

Incident Ray Reflected Ray

qi qr

Refraction At the surface of transparent media, glass,

water etc both reflection and refraction occur.

Normal Incident Ray

Reflected Ray

Refracted Ray

Medium 1

Medium 2

q1

q2

q1

Light ray changes direction going from one

medium to another.

Which way does it bend and by how much?

Is q2<q1 or is q2>q1

Refraction (deflection from a straight path in

passing obliquely from one medium

( such as air) into another (such as glass)

Answer

Depends on the speed of light in both media

q2

Refraction

Refraction analogy

Smooth concrete

grass

Rolling barrel

speed of light in

the material = v

Index of refraction (n) of the medium

cn

v

The amount by which a medium reduces the

speed of light is characterised by

Vacuum 1(by definition)

Air 1.0003

Glass 1.52

Water 1.33

Diamond 2.42

Indices of Refraction

Refraction

Speed of light in a vacuum: c = 3x108 ms-1

Example

Calculate the speed of light in diamond

8 18 13 10

1.24 102.42

c msv ms

n

Refraction

Example

How long does it take light to travel

394cm in glass

8 18 13 10

1.97 101.52

msv ms

8

8 1

3.942 10

1.97 10

mt s

ms

dt

v

Calculate the speed of light in glass

cv

n

Normal

q1

q2

Incident

Ray

Medium 1

Medium 2

q1

q2

n2 > n1 n2 < n1

1 1

2 2

Sin v

Sin v

q

q

1 1

2 2

/

/

Sin c n

Sin c n

q

q

1 2

2 1

Sin n

Sin n

q

q

1 1 2 2n Sin n Sinq q

where v1 and v2 are the

speeds of light in media

1 and 2 respectively

Monochromatic light (one colour or frequency)

Refraction

Normal

Incident

Ray

cn

v

Refraction

product nSinq remains constant as

light crosses a boundary from

one medium to another

Incident and refracted rays and the normal

are all in the same plane

1 1 2 2n Sin n Sinq q

Law of refraction or Snell’s law

Example

A laser beam is directed upwards from below

the surface of a lake at an angle of 35º to the

vertical. Determine the angle at which the light

emerges into the air. n1(air) =1.0003 and

n2 (water) =1.33

1 1 2 2n Sin n Sinq q

0

11.0003 1.33 35Sin Sinq

Normal

air

water

q1 n1

n2

Snell’s law

0

1

1

0

1

1.33 35

1.0003

0.76

49.7

SinSin

Sin

q

q

q

35º

If light enters the water at an angle of 49.70,

what is its refraction angle in the water?

Normal

Incident

Ray

Medium 1

Medium 2

q1

q2

n2 > n1

n2 < n1

1 1 2 2n Sin n Sinq q

Monochromatic light (one colour or frequency)

n2 > n1

or

Normal incidence q1 = 0

therefore q2 = 0.

transmitted ray is not deviated

independent of the materials on either

side of the interface.

Refraction

Incident

Ray

End of ruler

air

water

ruler

Apparent position

of ruler end

Refraction

Real and apparent depth

Ruler partially immersed in water

Setting sun appears flattened (top to bottom)

because light from lower part of the sun

undergoes greater refraction upon passing

through denser air (higher refractive index)

in lower part of the Earth’s atmosphere.

Refraction

2

2 1

cSin n

Sin n

q

q

Angle of incident for which refracted ray emerges

tangent to the surface is called the critical angle

Refraction

Critical Angle

as q1 is increased q2 increases

q1

q2

n2 < n1

q2 900

qc >qc

qc is critical angle

1

2

in this case q2 = 90o or Sin q2 =1

2

1

c

nSin

nq

2

1

c

nSin

nq

1 cq q>

incident ray undergoes total internal

reflection at boundary and cannot

pass into the material with the lower

refractive index

Refraction

Total internal reflection

q1

q2

n2 < n1

q2 900

qc >qc

qc is critical angle

1

2

Ray undergoes

total internal

reflection

maximum value of the sine of any angle is 1

total internal reflection occurs at interface only

when n2 < n1

when

1cSinq

Example

1 1 02

1

1.0003sin sin 49

1.33c

n

nq

Determine the critical angle for both water and

diamond with respect to air.

1 1 02

1

1.0003sin sin 24.4

2.42c

n

nq

water

diamond

Refraction

2

1

c

nSin

nq

45º

1 1 02

1

1.33sin sin 61

1.52c

n

nq

Refractive index of glass =1.52

Refractive index of air =1.0003

Total internal reflection

at glass air interface if

incident angle is >410

Glass prism

(right angled

isosceles triangle)

What happens the beam if the prism is immersed

in water? Refractive index of water =1.33

1 1 02

1

1.0003sin sin 41

1.52c

n

nq

Example

qc > 45º

Total internal reflection

at glass-water interface does not occur

What happens to light ray at the glass-air

interface in prism as shown.

Critical angle given by

45º

Applications

Fibre optic cables used for telecommunications

and for diagnostic tools in medicine

Refraction

Total internal reflection

Optical fibre

(end on)

Refractive index of core greater than

refractive index of clading

Light coupled into core will travel extremely

long distances along fibre, undergoing

total internal reflection at core-cladding

interface and exit only at the other end.

diameter of core 8mm

350

q4

glass

q2

q3

air

air

Light in air is incident on a glass block at an

angle of 350 The sides of the glass block are

parallel. At what angle does the light emerge

into the air from the lower surface of the glass

block?

glass block has

parallel sides,

therefore

q2 q3 =

0

4

0

4

35

35

Sin Sinq

q

Example

Let n1 = refractive index of air

& n2 = refractive index of glass Using Snell’s

Law 0

1 2 235n Sin n Sinq

2 3 1 4n Sin n Sinq q

2 2 1 4n Sin n Sinq q q2 Since q3 =

0

1 135 4n Sin n Sinq

Infrared Ultra violet Wavelength

Visible spectrum

v f Electromagnetic wave

Transverse wave

V: velocity

f: frequency

: wavelength

Light: Electromagnetic wave

Electromagnetic wave

Unpolarised light

viewed along

direction of

propagation

Polarised Light

polarised light

viewed along

direction of

propagation

Light source

Light beam Polariser

Light waves

vertically polarised

Schematic representation

Polaroid

filter Unpolarised

light

Polarised

light

Polarised Light

Unpolarised

light

Schematic representation

Polarised

light

Vertically polarised

light wave

Unpolarised

Incident beam

Horizontal

polariser

Vertical

polariser

Polarising

filter

Light can become polarised by

•Reflection •refraction •scattering

Unpolarised incident

light

Polarised reflected

light

Polarised incident

light

Polarised reflected

light

Polarised incident

light No reflected

light

Polarised Light

?

?

Polarised Light

Applications 3D movies

2 slightly different images projected on screen

2 cameras, a short distance apart,

photograph original scene

Each image linearly polarised in

mutually perpendicular direction

3D glasses have perpendicular polarisation axis

Each eye sees a different image associated with

different viewing angle from each camera

Brain perceives the compound image

as having depth or three dimensions.

Polarisation of light : application

Demineralised enamel is polarisation sensitive

shading may be seen, indicating the early

stages of caries at the tooth’s surface

Application to dentistry

Early detection of caries

Demineralised enamel viewed directly with

unpolarised light

No information

Polarised light incident on the dental tissue

Visual, mechanical probing, x rays???

The wavelength of red light from a HeNe laser is 633 nm

but is 474 nm in the aqueous humor inside an eyeball.

Calculate the index of refraction of the aqueous humor and

the speed and frequency of the light in the substance.

0

0

633

6331.34

474

n

nmn

nm

8 18 13 10

2.25 101.34

c x msv x ms

n

8 114

9

2.25 104.75 10

474 10

v x msf x Hz

x m

8 114

0 9

0

3.00 104.75 10

633 10

c x msf x Hz

x m

Refractive index

Speed in aqueous humor

Frequency of the light in aqueous humor

Frequency of the light in air

Example

0fcn

v f

0c f