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Chapter 24 Wave Optics

# Chapter 24 Wave Optics. General Physics Review – waves T=1/f period, frequency T=1/f period, frequency v = f velocity, wavelength v = f velocity, wavelength

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### Text of Chapter 24 Wave Optics. General Physics Review – waves T=1/f period, frequency T=1/f period,... Chapter 24

Wave Optics General Physics

Review – wavesReview – waves T=1/fT=1/f

period, frequencyperiod, frequency v = v = f f

velocity, wavelengthvelocity, wavelength

Huygen’s principleHuygen’s principle DiffractionDiffraction

SuperpositionSuperposition InterferenceInterference

Reflection/TransmissionReflection/Transmission Phase changePhase change

Transverse waveTransverse wave PolarizationPolarization

wavelength

phase amplitude General Physics

Diffraction Huygens’ principle

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

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

occurs when waves pass through small openings, around obstacles or by sharp edges General Physics

Diffraction and InterferenceDiffraction and Interference

Sections 6 – 8Sections 6 – 8 General Physics

Diffraction Grating

The diffracting grating consists of many equally spaced parallel slits of width dA typical grating contains several

thousand lines per centimeterThe intensity of the pattern on the

screen is the result of the combined effects of interference and diffraction General Physics

Diffraction Grating, 2

The condition for maxima isd sin θbright = m λ

m = 0, 1, 2, … The integer m is the order

number of the diffraction pattern

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

Diffraction Grating, 3 All the wavelengths are

focused at m = 0 This is called the zeroth

order maximum The first order maximum

corresponds to m = 1 Note the sharpness of the

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

broad, bright fringes characteristic of the two-slit interference pattern

Active Figure: The Diffraction Grating General Physics

Which color will diffract Which color will diffract largest angle (m=1)largest angle (m=1)

in a diffraction grating?in a diffraction grating?

33% 33%33%

10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

1.1. Red (700 nm)Red (700 nm)

2.2. Green (550 nm)Green (550 nm)

3.3. Blue (460 nm)Blue (460 nm)

d sin θbright = m λ General Physics

Diffraction Grating Spectrometer

The emission spectrum for hydrogen contains four visible wavelengths

All wavelengths are focused at m = 0

For higher orders, each wavelength deviates through a specific angle

Each order contains the four wavelengths

Active Figure: The Diffraction Grating Spectrometer General Physics

Single-Slit Diffraction A single slit placed between a

distant light source and a screen produces a diffraction pattern It will have a broad, intense central

band – central maximum The central band will be flanked by a

series of narrower, less intense secondary bands – secondary maxima

The central band will also be flanked by a series of dark bands – minima

The results of the single slit cannot be explained by geometric optics Geometric optics would say that light

rays traveling in straight lines should cast a sharp image of the slit on the screen General Physics

Single-Slit Diffraction

Fraunhofer Diffraction occurs when the rays leave the diffracting object in parallel directions Screen very far from the slit Converging lens (shown)

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

Single-Slit Diffraction According to Huygens’ principle,

each portion of the slit acts as a source of waves

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

All the waves that originate at the slit are in phase

Wave 1 travels farther than wave 3 by an amount equal to the path difference δ = (a/2) sin θ

Similarly, wave 3 travels farther than wave 5 by an amount equal to the path difference δ = (a/2) sin θ General Physics

Single-Slit Diffraction

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

δ = ½ λ = (a/2) sin θ -» sin θ = λ / a

In general, destructive interference occurs for a single slit of width a when

sin θdark = mλ / a m = 1, 2, 3, … General Physics

Single-Slit Diffraction

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

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

ym = L tan θdark , where sin θdark = mλ / a

Active Figure: Fraunhofer Diffraction Pattern for a Single Slit General Physics

Reflection and InterferenceReflection and InterferencePhase ChangePhase Change

Sections 2, 6 – 8Sections 2, 6 – 8 General Physics

Phase Change Due To Reflection

An electromagnetic wave undergoes a phase change of 180° upon reflection from a medium of higher index of refraction than the one in which it was traveling Analogous to a reflected pulse on a string General Physics

No Phase Changes Due To Reflection

There is no phase change when the wave is reflected from a medium of lower index of refraction than the one in which it was traveling Analogous to a pulse in a string reflecting from a free support General Physics

Lloyd’s Mirror

An arrangement for producing an interference pattern with a single light source

Waves reach point P either by a direct path or by reflection

The reflected ray can be treated as a ray from the source S’ behind the mirror General Physics

Interference Pattern from the Lloyd’s Mirror

An interference pattern is formed

The positions of the dark and bright fringes are reversed relative to pattern of two real sources

This is because there is a 180° phase change produced by the reflection General Physics

Thin FilmsThin Films 180 180180 180 180

0

0

0

0

incident wave

refl. refl./trans.

trans.

trans.trans.

refl.trans.

refl./trans.

trans. refl.

trans. refl.

trans.trans.

refl.trans. refl./trans.

destructiveinterference

destructiveinterference

constructiveinterference

constructiveinterference 180 180180 180 180

180

180

180

180

incident wave

inc.

trans.

trans.trans.

refl.trans.

trans. refl.trans./refl.

trans.trans.

constructiveinterference

constructiveinterference

destructiveinterference

destructiveinterference

trans./refl.

refl.trans. refl.trans.trans./refl.refl. General Physics

PolarizationPolarization

Section 9Section 9 General Physics

Polarization of Light Waves

Each atom produces a wave with its own orientation of

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

This is an unpolarized wave

E General Physics

Polarization of Light, cont

A wave is said to be linearly polarized if the resultant electric field vibrates in the same direction at all times at a particular point

Polarization can be obtained from an unpolarized beam by Selective absorption Reflection Scattering General Physics

E. H. Land discovered a material that polarizes light through selective absorptionHe called the material PolaroidThe molecules readily absorb light

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

Polarization by Selective Absorption General Physics

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

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

Selective Absorption, cont General Physics

Selective Absorption, final

The intensity of the polarized beam transmitted through the second polarizing sheet (the analyzer) varies as I = Io cos2 θ

Io is the intensity of the polarized wave incident on the analyzer

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

Active Figure: The Linear Polarizer General Physics

Polarization by Reflection

When an unpolarized light beam is reflected from a surface, the reflected light is Completely polarized Partially polarized Unpolarized

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

unpolarized For angles between this, there is some degree of

polarization For one particular angle, the beam is completely

polarized General Physics

Polarization by Reflection, cont

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

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

θp may also be called Brewster’s Angle

sintan

cosp

pp

n General Physics

Polarization by Scattering

When light is incident on a system of particles, the electrons in the medium can absorb and reradiate part of the lightThis process is called scattering

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

Polarization of Sunlight by Scattering

Unpolarized sunlight is incident on an air molecule

The horizontal part of the electric field vector in the incident wave causes the charges to vibrate horizontally

The vertical part of the vector simultaneously causes the charges to vibrate vertically

Horizontally polarized waves are emitted downward toward the observer

Vertically polarized waves are emitted parallel to the Earth General Physics

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