Chapter 24 The Wave Nature of Light

Chapter 24The Wave Nature

of Light

AP Physics BMrs. Wallace

24-01 Conditions for Interference

24-02 Young’s Double-Slit Experiment

24-03 Change of Phase Due to Reflection

24-04 Interference in Thin Films

24-06 Diffraction

24-07 Single-Slit Diffraction

24-08 The Diffraction Grating

Wave Optics

Sections

Wave Optics 24 (02 of 41)

Conditions for Interference

For observable interference effects, sources must be

1. Coherent

2. Monochromatic

Waves must maintain a constant phase

relationship

Waves must have the same wavelength


Chapter 24: Wave Optics

Two light sources are said to be coherent if they

(A) are of the same frequency.

(B) are of the same frequency, and maintain a constant phase difference.

(C) are of the same amplitude, and maintain a constant phase difference.

(D) are of the same frequency and amplitude.


If light is a wave, interference effects will be seen, where one part of wavefront can interact with another part.

One way to study this is to do a double-slit experiment:

Young’s Double-Slit Experiment




The interference occurs because each point on the screen is not the same distance from both slits. Depending on the path length difference, the wave can interfere constructively (bright spot) or destructively (dark spot).




What principle is responsible for alternating light and dark bands when light passes through two or more narrow slits?

(A) refraction

(B) polarization

(C) dispersion

(D) interference


We can use geometry to find the conditions for constructive and destructive interference:

.... 2, 1, ,0m ,λmθsind

Bright(constructive interference)

.... 2, 1, ,0m ,λ mθsind21

Dark(destructive interference)



S1

S2

PS2 - PS1= d sin()

Constructive Interference

. . . 2, 1, ,0m λm)θsin(d

Destructive Interference

. . . 2, 1, ,0m λ 21

m)θsin(d

screen

P

d



S1

S2

screen

Bright

d

y

L

Ly

)θtan()θsin(

dλmL

y )bright(

Constructive Interference

dλL

yΔ

2, 1, ,0m λmθsind



S1

S2

d

screen

Dark

Ly

)θtan()θsin(

dλL

yΔ

L

y

d

λL21

my dark

Destructive Interference

. . . 2, 1, ,0m

21

m)θsin(d




In a Young's double slit experiment, if the separation between the slits decreases, what happens to the distance between the interference fringes?

(A) It decreases.

(B) It increases.

(C) It remains the same.

(D) There is not enough information to determine.

dλL

yΔ



At the first minima on either side of the central bright spot in a double-slit experiment, light from each opening arrives

(A) in phase.

(B) 90° out of phase.

(C) 180° out of phase.

(D) none of the given answers



At the second maxima on either side of the central bright spot in a double-slit experiment, light from

(A) each opening travels the same distance.

(B) one opening travels twice as far as light from the other opening.

(C) one opening travels one wavelength of light farther than light from the other opening.

(D) one opening travels two wavelengths of light farther than light from the other opening.



What principle is responsible for light spreading as it passes through a narrow slit?

(A) refraction

(B) polarization

(C) diffraction

(D) interference


Diffraction


The resulting pattern of light and dark stripes is called a diffraction pattern.

This pattern arises because different points along a slit create wavelets that interfere with each other just as a double slit would.

The minima of the single-slit diffraction pattern occur when

.... ,3 ,2 ,1m

λmθsin D

Single-Slit Diffraction


d

L dλ2

2

dλ

1

dλ

1

dλ2

2

θsin y

θsin y

0θsin 0

θsin y

θsin y




A person gazes at a very distant light source. If she now holds up two fingers, with a very small gap between them, and looks at the light source, she will see

(A) the same thing as without the fingers, but dimmer.

(B) a series of bright spots.

(C) a sequence of closely spaced bright lines.

(D) a hazy band of light varying from red at one side to blue or violet at the other.


dλ

θsin

Ly

θtan

θtanθsin

Ly

dλ

dλL

y

m 10x 3.00

m 10x5.6m 5.24

7

m 0.0054y

yd

A single slit of width 0.30 mm is illuminated with 650 nm light. Aninterference pattern is formed on a screen 2.5 m away. Find the distancefrom the first dark band to the centralbright band.



2 m λmθsin D

A single slit of width 0.14 mm is illuminated by monochromatic light and interference bands are observed on a screen 2.0 m away.If the second dark band is 16 mm from the central bright band,what is the wavelength of the light?

D

L

y

Dλ2

θsin

θsinLy

θtan Dλ2

Ly

L2yD

λ m 0.22

m 00014.0m 016.0

nm 560 m 10 x 6.5λ 7



A diffraction grating consists of a large number of equally spaced narrow slits or lines. A transmission grating has slits, while a reflection grating has lines that reflect light.

The more lines or slits there are, the narrower the peaks.

Two slits

Six slits

The Diffraction Grating



Consider two diffraction gratings with the same slit separation, one grating has 3 slits and the other 4 slits. If both gratings are illuminated with a beam of the same monochromatic light, make a statement concerning the separation between the orders.

(A) The grating with 3 slits produces the greater separation between orders.

(B) The grating with 4 slits produces the greater separation between orders.

(C) Both gratings produce the same separation between orders.

(D) Both gratings produce the same separation between orders, but the orders are better defined with the 4-slit grating.


The maxima of the diffraction pattern are defined by

...... 3, 2, 1, ,0m ,λmθsind



A 3500-line/cm grating produces a third-order fringe at a 28.0o angle. What is the wavelength of light being used?

λmθsind

mθsind

λ

3

0.28sin

mlines

000,350

1

λ

o

m 10 x 47.4 7

mn 447

The Diffraction Grating (Problem)


A diffraction grating has 6.0 x 105 lines/m. Find the angular spread in second-order spectrum between red light of wavelength

7.0 x 107 m and blue light of wavelength 4.5 x 107 m.RB

R

B

m = 2

line/m 10 x 0.6

1m 10 x 0.72

sinθ

5

71

R o1.57

line/m 10 x 0.6

1m 10 x 5.42

sinθ

5

71

Bo7.32

ooo 4.24 7.321.57θΔ

λmθsind

The Diffraction Grating (Problem)


A spectrometer makes accurate measurements of wavelengths using a diffraction grating or prism.

The Spectrometer and Spectroscopy



The wavelength can be determined to high accuracy by measuring the angle at which the light is diffracted.

Atoms and molecules can be identified when they are in a thin gas through their characteristic emission lines.

θsinmd

λ

The Spectrometer and Spectroscopy



Change of Phase Due to Reflection

A reflected light wave undergoes a phase change of 180o.


Change of Phase Due to Reflection

A reflected light wave undergoes no phase change.



When a beam of light, which is traveling in glass, strikes an air boundary, there is

(A) a 90° phase change in the reflected beam.

(B) a 180° phase change in the reflected beam.

(C) a 45° phase change in the reflected beam.

(D) no phase change in the reflected beam.


glass

air

air

Another way path lengths can differ, and waves interfere, is if they travel through different media.

If there is a very thin film of material – a few wavelengths thick – light will reflect from both the bottom and the top of the layer, causing interference.

This can be seen in soap bubbles and oil slicks, for example.

changephase

λ 21

changephase

oN

Interference in Thin Films


t

(maxima)Bright λt

(minima) Dark λt

If

41

21



t

a

bThe phase displacement of (b) relative to (a) is

reflection to Due λ21

difference path to Due tn2

m ... , , , is tn2 When21

25

23

21

21

m ... ,3 ,2 , is tn2 When21

There is darkness

There is brightness

n



n = 1.0

a

b

air

kerosene

water

n’ = 1.2

n’’ = 1.3

t

A tanker has dumped a large quantity of kerosene into the gulf creating a large slick on the top of the water. You are looking straight down from an airplane onto a region of the slick where its thickness is t = 460 nm.Which wavelength of visible light is reflected the greatest?

λmtn'2

mtn'2

λ

m

2.1 nm 6042λ

nm 1104λ 1m

nm 552λ 2m

nm 368λ 3m

Interference in Thin Films (Problem)


A tanker has dumped a large quantity of kerosene into the gulf creating a large slick on the top of the water. You are a scuba-diver directly under the slick where its thickness is t = 460 nm.Which wavelength of visible light is the transmitted intensitythe greatest?

λmtn'2λ21

21m

tn'2λ

21m

2.1nm 6042λ

nm 2208λ 1m

nm 736λ 2m

nm 441λ 3m

n = 1.0

a b

air

kerosene

water

n’ = 1.2

n’’ = 1.3

t

nm 315λ 4m



One can also create a thin film of air by creating a wedge-shaped gap between two pieces of glass.



BRIGHT

BRIGHT

DARK

0 t 2λ

t λ t

21

mt2 Dark21

m = 0 m = 1 m = 2

DARK

DARK



Problem Solving: Interference

Interference occurs when two or more waves arrive simultaneously at the same point in space.

Constructive interference occurs when the waves are in phase.

Destructive interference occurs when the waves are out of phase.

An extra half-wavelength shift occurs when light reflects from a medium with higher refractive index.



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Chapter 24 The Wave Nature of Light