24.6 Diffraction24.6 Diffraction Huygen’s principle Huygen’s principle

requires that the requires that the waves spread out after waves spread out after they pass through slitsthey pass through slits

This spreading out of This spreading out of light from its initial line light from its initial line of travel is called of travel is called diffractiondiffraction In general, diffraction In general, diffraction

occurs when wave pass occurs when wave pass through small openings, through small openings, around obstacles or by around obstacles or by sharp edgessharp edges

Diffraction, 2Diffraction, 2

A single slit placed between a distant A single slit placed between a distant light source and a screen produces a light source and a screen produces a diffraction patterndiffraction pattern It will have a broad, intense central bandIt will have a broad, intense central band The central band will be flanked by a The central band will be flanked by a

series of narrower, less intense series of narrower, less intense secondary bandssecondary bands

Called secondary maximaCalled secondary maxima The central band will also be flanked by The central band will also be flanked by

a series of dark bandsa series of dark bands Called minimaCalled minima

Diffraction, 3Diffraction, 3 The results of the The results of the

single slitsingle slit cannot cannot be explained by be explained by geometrical opticsgeometrical optics Geometrical optics Geometrical optics

would say that would say that light rays traveling light rays traveling in straight lines in straight lines should cast a should cast a sharp image of the sharp image of the slit on the screenslit on the screen

Fresnel and Fraunhofer Fresnel and Fraunhofer DiffractionDiffraction

Relation of Fresnel diffraction to Fraunhofer Relation of Fresnel diffraction to Fraunhofer diffraction by a single slitdiffraction by a single slit

Fresnel Fraunhofer

Parallel rays

Fraunhofer DiffractionFraunhofer Diffraction

Fraunhofer Fraunhofer DiffractionDiffraction occurs occurs when the rays leave when the rays leave the diffracting object the diffracting object in parallel directionsin parallel directions

A bright fringe is A bright fringe is seen along the axis seen along the axis ((θθ = 0) with = 0) with alternating bright alternating bright and dark fringes on and dark fringes on each sideeach side

24.7 Single Slit 24.7 Single Slit DiffractionDiffraction

According to Huygen’s According to Huygen’s principle, each portion of principle, each portion of the slit acts as a source of the slit acts as a source of waveswaves

The light from one portion The light from one portion of the slit can interfere of the slit can interfere with light from another with light from another portionportion

The resultant intensity on The resultant intensity on the screen depends on the the screen depends on the direction direction θθ

w/2

w

w

w

Single Slit Diffraction, 2Single Slit Diffraction, 2

All the waves that originate at the slit are in All the waves that originate at the slit are in phasephase

Wave 1 travels farther than wave 3 by an Wave 1 travels farther than wave 3 by an amount equal to the path difference (amount equal to the path difference (ww/2)sin/2)sinθθ

If this path difference is exactly half of a If this path difference is exactly half of a wavelength, the two waves cancel each other wavelength, the two waves cancel each other and destructive interference resultsand destructive interference results

In general, In general, destructive interferencedestructive interference occurs for occurs for a single slit of width a single slit of width ww when when sinsinθθdarkdark==nλnλ / /ww nn = = 1, 1, 2, 2, 3, … 3, …

Single Slit Diffraction, 3Single Slit Diffraction, 3 The general features of The general features of

the intensity distribution the intensity distribution are shownare shown

A broad central bright A broad central bright fringe is flanked by much fringe is flanked by much weaker bright fringes weaker bright fringes alternating with dark alternating with dark fringesfringes

The points of constructive The points of constructive interference lie interference lie approximately halfway approximately halfway between the dark fringesbetween the dark fringes

w

w

w

w

QUICK QUIZ 24.1

In a single-slit diffraction experiment, as the width of the slit is made smaller, the width of the central maximum of the diffraction pattern becomes (a) smaller, (b) larger, or (c) remains the same.

Diffraction GratingsDiffraction Gratings

The diffracting grating consists of The diffracting grating consists of many equally spaced parallel slitsmany equally spaced parallel slits A typical grating contains several A typical grating contains several

thousand lines per centimeterthousand lines per centimeter The intensity of the pattern on the The intensity of the pattern on the

screen is the result of the screen is the result of the combined effects of interference combined effects of interference and diffractionand diffraction

Diffraction Grating, cont.Diffraction Grating, cont. The condition for The condition for maximamaxima is is

d d sinsinθθbrightbright==mλmλmm=0, 1, 2, …=0, 1, 2, …

The integer The integer mm is the is the order order numbernumber of the diffraction of the diffraction patternpattern

If the incident radiation If the incident radiation contains several wavelengths, contains several wavelengths, each wavelength deviates each wavelength deviates through a specific anglethrough a specific angle

Diffraction Grating, cont.Diffraction Grating, cont. All the wavelengths are All the wavelengths are

focused at focused at mm = 0 = 0 This is called the zeroth- order This is called the zeroth- order

maximummaximum The first order maximum The first order maximum

corresponds to corresponds to mm = 1 = 1 Note the sharpness of the Note the sharpness of the

principle maxima and the principle maxima and the broad range of the dark broad range of the dark areaarea This is in contrast to the broad, This is in contrast to the broad,

bright fringes characteristic of bright fringes characteristic of the two-slit interference the two-slit interference patternpattern

Grating spectrometerGrating spectrometer

The light to be The light to be analyzed passes analyzed passes through a slit and is through a slit and is formed into a parallel formed into a parallel beam by a lens. The beam by a lens. The diffracted light leaves diffracted light leaves the grating at angles the grating at angles that satisfy that satisfy d d sinsinθθbrightbright==mλmλ

Diffraction Grating in CD Diffraction Grating in CD TrackingTracking A diffraction grating A diffraction grating

can be used in a three-can be used in a three-beam method to keep beam method to keep the beam on a CD on the beam on a CD on tracktrack

The central maximum The central maximum of the diffraction of the diffraction pattern is used to read pattern is used to read the information on the the information on the CDCD

The two first-order The two first-order maxima are used for maxima are used for steeringsteering

24.9 Polarization of 24.9 Polarization of Light WavesLight Waves Each atom of a light Each atom of a light

source produces a wave source produces a wave with its own orientation with its own orientation of of EE

All directions of the All directions of the electric field electric field EE vector vector are equally possible and are equally possible and lie in a plane lie in a plane perpendicular to the perpendicular to the direction of propagationdirection of propagation

This is an This is an unpolarized unpolarized wavewave

Polarization of Light, cont.Polarization of Light, cont. A wave is said to be A wave is said to be linearly linearly

polarizedpolarized if the resultant if the resultant electric field electric field vibratesvibrates in the in the same direction at all timessame direction at all times at a particular pointat a particular point

Polarization can be obtained Polarization can be obtained from an unpolarized beam from an unpolarized beam by by selective absorptionselective absorption reflectionreflection scatteringscattering

Polarization Features, Polarization Features, SummarySummary

(a) When the vectors are (a) When the vectors are randomly oriented, the randomly oriented, the light is light is unpolarizedunpolarized (natural light). (b) With (natural light). (b) With preferential orientation preferential orientation of the field vectors, the of the field vectors, the light is light is partially partially polarized.polarized. (c) When the (c) When the vectors are in one plane, vectors are in one plane, the light is the light is linearly linearly polarizedpolarized. .

Polarization by Selective Polarization by Selective AbsorptionAbsorption

The most common technique for polarizing lightThe most common technique for polarizing light Uses a material that transmits waves whose Uses a material that transmits waves whose

electric field vectors in the plane parallel to a electric field vectors in the plane parallel to a certain direction and absorbs waves whose certain direction and absorbs waves whose electric field vectors are perpendicular to that electric field vectors are perpendicular to that directiondirection

Polarization by Selective Polarization by Selective Absorption, “Rope Model”Absorption, “Rope Model”

The principle of polarization: A transverse wave is The principle of polarization: A transverse wave is linearly polarized when its vibrations always occur along linearly polarized when its vibrations always occur along one direction. (a) The rope passes a slit parallel to the one direction. (a) The rope passes a slit parallel to the vibrations, but (b) does not pass through a slit that is vibrations, but (b) does not pass through a slit that is perpendicular to the vibrations. perpendicular to the vibrations.

Selective Absorption, cont.Selective Absorption, cont.

E. H. Land discovered a material E. H. Land discovered a material that polarizes light through that polarizes light through selective absorptionselective absorption He called the material He called the material polaroidpolaroid The oriented molecules readily absorb The oriented molecules readily absorb

light whose electric field vector is light whose electric field vector is parallel to their lengths and transmit parallel to their lengths and transmit light whose electric field vector is light whose electric field vector is perpendicular to their lengthsperpendicular to their lengths

Selective Absorption, finalSelective Absorption, final

The intensity of the polarized beam The intensity of the polarized beam transmitted through the second transmitted through the second polarizing sheet (the analyzer) varies polarizing sheet (the analyzer) varies asas II = = IIoo cos cos22 θθ

IIoo is the intensity of the is the intensity of the polarized wave polarized wave incident on the analyzerincident on the analyzer

This is known as This is known as Malus’ LawMalus’ Law and applies to any and applies to any two polarizing materials whose transmission two polarizing materials whose transmission axes are at an angle of axes are at an angle of θθ to each other to each other

Polarization by ReflectionPolarization by Reflection When an unpolarized light beam is reflected When an unpolarized light beam is reflected

from a surface, the reflected light isfrom a surface, the reflected light is Completely polarizedCompletely polarized Partially polarizedPartially polarized UnpolarizedUnpolarized

It depends on the angle of incidenceIt depends on the angle of incidence If the angle is 0° or 90°, the reflected beam is If the angle is 0° or 90°, the reflected beam is

unpolarizedunpolarized For angles between this, there is some degree of For angles between this, there is some degree of

polarizationpolarization For one particular angle, the reflected beam is For one particular angle, the reflected beam is

completely polarizedcompletely polarized

Polarization by Reflection, Polarization by Reflection, cont. cont.

22=90=90oo--pp

Snells law Snells law   

sinsinpp/sin(90/sin(90oo--pp)=sin)=sinpp/cos/cospp==nn22//nn11

nn11=1 (air)=1 (air)

tantanpp==nn22==nn

Brewster angle

Polarization by Reflection, Polarization by Reflection, SummarySummary

The angle of incidence for which the The angle of incidence for which the reflected beam is completely polarized is reflected beam is completely polarized is called the called the polarizing anglepolarizing angle, , θθpp

Brewster’s Law relates the polarizing Brewster’s Law relates the polarizing angle to the index of refraction for the angle to the index of refraction for the materialmaterial

θθpp may also be called may also be called Brewster’s AngleBrewster’s Angle

pp

p tancos

sin

n

Polarization by ScatteringPolarization by Scattering

When light is incident on a system When light is incident on a system of particles, such as a gas, the of particles, such as a gas, the electrons in the medium can absorb electrons in the medium can absorb and reradiate part of the lightand reradiate part of the light This process is called This process is called scatteringscattering

An example of scattering is the An example of scattering is the sunlight reaching an observer on sunlight reaching an observer on the earth becoming polarizedthe earth becoming polarized

Polarization by Scattering, Polarization by Scattering, cont.cont. The horizontal part of the The horizontal part of the

electric field vector in the electric field vector in the incident wave causes the incident wave causes the charges to vibrate charges to vibrate horizontallyhorizontally

The vertical part of the The vertical part of the vector simultaneously vector simultaneously causes them to vibrate causes them to vibrate verticallyvertically

Horizontally and vertically Horizontally and vertically polarized waves are emittedpolarized waves are emitted

Optical ActivityOptical Activity

Certain materials display the Certain materials display the property of property of optical activityoptical activity A substance is optically active if it A substance is optically active if it

rotates the plane of polarization of rotates the plane of polarization of transmitted lighttransmitted light

Optical activity occurs in a material Optical activity occurs in a material because of an asymmetry in the because of an asymmetry in the shape of its constituent materialsshape of its constituent materials

Liquid CrystalsLiquid Crystals

A A liquid crystalliquid crystal is a substance with is a substance with properties intermediate between those of properties intermediate between those of a crystalline solid and those of a liquida crystalline solid and those of a liquid The molecules of the substance are more The molecules of the substance are more

orderly than those of a liquid but less than orderly than those of a liquid but less than those in a pure crystalline solidthose in a pure crystalline solid

To create a display, the liquid crystal is To create a display, the liquid crystal is placed between two polarizers and glass placed between two polarizers and glass plates and electrical contacts are made plates and electrical contacts are made to the liquid crystalto the liquid crystal

Liquid Crystals, cont.Liquid Crystals, cont.

Rotation of a polarized Rotation of a polarized light beam by a liquid light beam by a liquid crystal when the crystal when the applied voltage is zeroapplied voltage is zero

Light passes through Light passes through the polarizer on the the polarizer on the right and is reflected right and is reflected back to the observer, back to the observer, who sees the segment who sees the segment as being brightas being bright

Liquid Crystals, cont.Liquid Crystals, cont.

When a voltage is When a voltage is applied, the liquid applied, the liquid crystal does not crystal does not rotate the plane of rotate the plane of polarizationpolarization

The light is absorbed The light is absorbed by the polarizer on by the polarizer on the right and none is the right and none is reflected back to the reflected back to the observerobserver

The segment is darkThe segment is dark

Liquid Crystals, finalLiquid Crystals, final

Changing the applied Changing the applied voltage to the crystal voltage to the crystal in a precise pattern in a precise pattern and at precise time and at precise time can make the can make the pattern tick of the pattern tick of the seconds on a watch, seconds on a watch, display a letter on display a letter on computer displays, computer displays, and so forthand so forth