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CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
College Physics B - PHY2054C
Wave Optics: Diffraction
10/29/2014
My Office Hours:Tuesday 10:00 AM - Noon
206 Keen Building
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Outline
1 Review: Thin-Film Interference
2 Single-Slit Experiment
3 Double-Slit ExperimentYoung ExperimentDouble-Slit Analysis
4 Single-Slit Interference
5 Diffraction Grating
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Thin-Film Interference
Assume a thin soap film rests on a flat glass surface.
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Thin-Film Interference
Assume a thin soap film rests on a flat glass surface.
The upper surface of the soap film is similar to the beam splitterin the interferometer:
• It reflects part of the incoming light and allows the rest tobe transmitted into the soap layer after refraction at theair-soap interface.
• The transmitted ray ispartially reflected at thebottom surface.
• The two outgoing rays meetthe conditions for interference:
1 Travel through different regions
2 Recombination
3 Coherence
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Thin-Film Interference
Assume a thin soap film rests on a flat glass surface.
Index of refraction of the film also needs to be accounted for:
• The wavelength changes as thelight wave travels from a vacuuminto the film:
λ film =vf
=c/n film
f
=λ vac
n film≈
λ air
n film
• Number of extra wavelengths:
N =2d
λ film=
2dλ/n film
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Frequency of Wave at Interface
When a light wave passes from one medium to another, thewaves must stay in phase at the interface. The frequency mustbe the same on both sides of the interface.
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Frequency of Wave at Interface
1 There is a phase change whenever the index of refractionon the incident side is less than the index of refraction ofthe opposite side (wave is inverted).
2 If the index of refraction is larger on the incident side thereflected ray in not inverted and there is no phase change.
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Phase Changes in a Thin Film
The total phase change in a thin film must be accounted for:
• The phase difference due to the extra distance traveledby the ray.
• Any phase change due to reflection.
• For a soap film on glass: n air < n film < n glass
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Phase Changes in a Thin Film
There are phase changes for both reflections at the soap filminterfaces:
B The reflections at both the top and bottom surfacesundergo a 180◦ phase change:
1 If the number of extra cycles, N, is an integer, there isconstructive interference: 2d = mλ/n film
2 If the number of extra cycles is a half-integer, there isdestructive interference: 2d = (m + 1/2)λ/n film
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Phase Changes in a Thin Film
Assume the soap bubble is surrounded by air.C There is a phase change at the top of the bubble. There
is no phase change at the bottom of the bubble:1 If the number of extra cycles, N, is a half-integer, there is
constructive interference: 2d = (m + 1/2)λ/n film
2 If the number of extra cycles is an integer, there isdestructive interference: 2d = mλ/n film
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Phase Changes in a Thin Film
Assume the soap bubble is surrounded by air.C There is a phase change at the top of the bubble. There
is no phase change at the bottom of the bubble:1 If the number of extra cycles, N, is a half-integer, there is
constructive interference: 2d = (m + 1/2)λ/n film
2 If the number of extra cycles is an integer, there isdestructive interference: 2d = mλ/n film
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Outline
1 Review: Thin-Film Interference
2 Single-Slit Experiment
3 Double-Slit ExperimentYoung ExperimentDouble-Slit Analysis
4 Single-Slit Interference
5 Diffraction Grating
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Light Through a Single Slit
Light passes through a slit or opening and illuminates a screen:
• As the width of the slit becomes closer to the wavelength ofthe light, the intensity pattern on the screen and additionalmaxima become noticeable.
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Single-Slit Diffraction
All types of waves undergo single-slit diffraction:
• Water waves have a wavelength easily visible.
• The outgoing wave front isapproximately spherical.
Diffraction is the bending orspreading of a wave when itpasses through an opening.
Wave Interference:http://phet.colorado.edu/en/simulation/wave-interference
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Huygens’s Principle
Christiaan Huygens(14 April 1629 - 8 July 1695)
Huygens’s Principle:All points on a wave frontcan be thought of as newsources of spherical waves.
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Outline
1 Review: Thin-Film Interference
2 Single-Slit Experiment
3 Double-Slit ExperimentYoung ExperimentDouble-Slit Analysis
4 Single-Slit Interference
5 Diffraction Grating
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Double-Slit Experiment
Light passes through two very narrow slits:
• When the two slits are both very narrow, each slit actsas a simple point source of new waves.
• The outgoing waves from each slit are like simplespherical waves.
• The double slit experiment showed conclusively that lightis a wave.
Why?XXXXXXX
?
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Question 1What will you observe on the screen in an experimentusing light incident on two slits?
A Nothing, the screen will be dark.
B A complicated pattern with numerous bright lines.
C Two bright lines corresponding to the number of slits.
D No changes compared to a single slit.
XXXXXXX
?
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Question 1What will you observe on the screen in an experimentusing light incident on two slits?
A Nothing, the screen will be dark.
B A complicated pattern with numerous bright lines.
C Two bright lines corresponding to the number of slits.
D No changes compared to a single slit.
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Double-Slit Experiment
Light passes through two very narrow slits:
• When the two slits are both very narrow, each slit actsas a simple point source of new waves.
• The outgoing waves from each slit are like simplespherical waves.
• The double slit experiment showed conclusively that lightis a wave (observation of interference).
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Question 2What will you observe on the screen in an experimentusing a beam of particles incident on two slits?
A Nothing, the screen will be dark.
B A complicated pattern with numerous bright lines.
C Two bright lines corresponding to the number of slits.
D No changes compared to a single slit.
XXXXXXX
?
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Young’s Double-Slit Experiment
Experiment was first carried out by T. Young around 1800:
• Light is incident onto two slits and after passing throughthem strikes a screen.
Experiment satisfies the general requirements for interference:
1 The interfering waves travel through different regions ofspace as they travel through different slits.
2 The waves come together at a common point on thescreen where they interfere.
3 The waves are coherent because they come from thesame source.
➜ Interference will determine how the intensity of light on thescreen varies with position.
Quantum Wave Interference:phet.colorado.edu/en/simulation/quantum-wave-interference
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Double-Slit Analysis
Determine the path length between each slit and the screen.
Assume W is very large. If the slits are separated by a distanced , then the difference in length between the paths of the tworays is:
∆L = d sin θ
Bright fringe:
d sin θ = m λ
m = 0, ± 1, ± 2, ...
Dark fringe:
d sin θ = (m +12)λ
m = 0, ± 1, ± 2, ...
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Double-Slit Intensity Pattern
The angle θ varies as you move along the screen:
• Each bright fringe corresponds to a different value of m.
• Negative values of m indicate that the path to those pointson the screen from the lower slit is shorter than the pathfrom the upper slit.
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
ExampleFor m = 1: sin θ = λ/d
• Since the angle is very small:
tanθ = θ and sin θ = θ and θ = λ/d
• Between m = 0 and m = 1: h = W tanθ = W λ/d
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
ExampleFor m = 1: sin θ = λ/d
• Since the angle is very small:
tanθ = θ and sin θ = θ and θ = λ/d
• Between m = 0 and m = 1: h = W tanθ = W λ/d
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
ExampleFor m = 1: sin θ = λ/d
• Since the angle is very small:
tanθ = θ and sin θ = θ and θ = λ/d
• Between m = 0 and m = 1: h = W tanθ = W λ/d
Suppose the slits are d = 0.1 mm apart and the screen islocated W = 50 cm from the slits. For light with a wavelengthof 630 nm:
h = Wλ
d= (0.5 m)
6.3 × 10−7 m1 × 10−4 m
= 3.2 mm
This fringe spacing is large enough to be seen easily by thenaked eye. This gives also a way to measure the wavelengthof light.
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Question 3
A Young’s double-slit experiment is performed in air andthen the apparatus is submerged in water. What happensto the fringe separation (d sin θ = m λ), and what can beused to explain the change, if any?
A The separation stays the as it is the sameexperiment independent of the medium.
B The separation decreases because the frequency ofthe light decreases in the water.
C The separation increases because the wavelength ofthe light increases in the water.
D The separation decreases because the wavelengthof the light decreases in the water.
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Question 3
A Young’s double-slit experiment is performed in air andthen the apparatus is submerged in water. What happensto the fringe separation (d sin θ = m λ), and what can beused to explain the change, if any?
A The separation stays the as it is the sameexperiment independent of the medium.
B The separation decreases because the frequency ofthe light decreases in the water.
C The separation increases because the wavelength ofthe light increases in the water.
D The separation decreases because the wavelengthof the light decreases in the water.
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Outline
1 Review: Thin-Film Interference
2 Single-Slit Experiment
3 Double-Slit ExperimentYoung ExperimentDouble-Slit Analysis
4 Single-Slit Interference
5 Diffraction Grating
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Single-Slit Interference
Slits may be narrow enough to exhibit diffraction but not sonarrow that they can be treated as a single point source ofwaves:
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Single-Slit Interference
Assume the single slit has a width, w . Light is diffracted as itpasses through the slit and then propagates to the screen:
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Single-Slit Interference
Assume the single slit has a width, w . Light is diffracted as itpasses through the slit and then propagates to the screen:
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Single-Slit Interference
Assume the single slit has a width, w . Light is diffracted as itpasses through the slit and then propagates to the screen.
All points across the slit act as wave sources andinterfere at the screen:
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Single-Slit Fringe Locations
If one point in each part of the slit satisfies the conditionsfor destructive interference (dark fringes), the waves from allsimilar sets of points will also interfere destructively:
w sin θ = ±m λ, with m = 1, 2, 3, ...
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Single-Slit Fringe Locations
If one point in each part of the slit satisfies the conditionsfor destructive interference (dark fringes), the waves from allsimilar sets of points will also interfere destructively:
w sin θ = ±m λ, with m = 1, 2, 3, ...
Different from doubleslits!
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Single-Slit Fringe Locations
There is no simple formula for the angles at which the brightfringes occur:
• There is a central bright fringe with other bright fringesthat are lower in intensity ➜ Central Maximum
About 20 times moreintense.
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Single-Slit: Central Maximum
The width of the central bright fringe isapproximately the angular separation ofthe first dark fringes on either side:
• The full angular width of thecentral bright fringe is 2λ/w .
• If the slit is much wider than thelight’s wavelength, the light beamessentially passes straight throughthe slit with almost no diffraction.
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Summary
The complete interference pattern that isproduced by two slits is combination of
A the double-slit pattern and
B the single-slit pattern.
C Intensity pattern for slits that arenot extremely narrow.
A full calculation of the intensity patternis very complicated.
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Outline
1 Review: Thin-Film Interference
2 Single-Slit Experiment
3 Double-Slit ExperimentYoung ExperimentDouble-Slit Analysis
4 Single-Slit Interference
5 Diffraction Grating
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Diffraction Grating
An arrangement of many slits is called a diffraction grating.
Assumptions:
1 The slits are narrow.
2 The screen is very faraway.
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Diffraction Grating
An arrangement of many slits is called a diffraction grating.
Assumptions:
1 The slits are narrow.
2 The screen is very faraway.
Since the screen is so faraway, the rays striking thescreen are approximatelyparallel making an angle θwith the horizontal axis:
∆L = d sin θ = m λ
Bright fringes:
m = 0, ± 1, ± 2, ...
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Diffraction Grating
The condition for bright fringes from a diffraction grating isidentical to the condition for constructive inteference from adouble slit:
• Overall intensity patterndepends on the numberof slits.
• The larger the numberof slits, the narrowerthe peaks.
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Diffraction Grating
A diffraction grating will produce an intensity pattern on thescreen for each color:
• The different colors will have different angles anddifferent places on the screen.
• Diffraction gratings are widely used to analyze the colorsin a beam of light.
CollegePhysics B
Review:Thin-FilmInterference
Single-SlitExperiment
Double-SlitExperimentYoung Experiment
Double-Slit Analysis
Single-SlitInterference
DiffractionGrating
Diffraction and CDs
Light reflected from the arcs in a CD actsas sources of Huygens waves:
• The reflected waves exhibitconstructive interference atcertain angles.
• Light reflected from a CD hasthe colors “separated”.