• textbook sections 28-1 -- 28-3 Physics 1161: Lecture 26 Interference
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• textbook sections 28-1 -- 28-3
Physics 1161: Lecture 26Interference
Superposition
t
+1
-1
t
+1
-1
t
+2
-2
+
Constructive Interference
In Phase
Superposition
t
+1
-1
t
+1
-1
t
+2
-2
+
Destructive Interference
Out of Phase
180 degrees
Which type of interference results from the superposition of the two waveforms shown?
1 2 3
0% 0%0%
1. Constructive2. Destructive3. Neither+
Different f
-1.5
-1
-0.5
0
0.5
1
1.5
-1.5
-1
-0.5
0
0.5
1
1.5
Which type of interference results from the superposition of the two waveforms shown?
1 2 3
0% 0%0%
1. Constructive2. Destructive3. Neither+
Different f
-1.5
-1
-0.5
0
0.5
1
1.5
-1.5
-1
-0.5
0
0.5
1
1.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
Interference for Light …• Can’t produce coherent light from separate
sources. (f 1014 Hz)
Single source
Two different paths
Interference possible here
• Need two waves from single source taking two different paths– Two slits– Reflection (thin films)– Diffraction*
Coherent & Incoherent Light
Double Slit Interference Applets
• http://www.walter-fendt.de/ph14e/doubleslit.htm
• http://vsg.quasihome.com/interfer.htm
Young’s Double Slit Applet
http://www.colorado.edu/UCB/AcademicAffairs/ArtsSciences/physics/PhysicsInitiative/Physics2000/applets/twoslitsa.html
Young’s Double Slit Layout
Interference - Wavelength
Light waves from a single source travel through 2 slits before meeting at the point shown on the screen. The interference will be:
1 2 3
0% 0%0%
1. Constructive2. Destructive3. It depends on L
Screen a distance L from slits
Single source of monochromatic light
d
2 slits-separated by d
L
Light waves from a single source travel through 2 slits before meeting at the point shown on the screen. The interference will be:
1 2 3
0% 0%0%
1. Constructive2. Destructive3. It depends on L
Screen a distance L from slits
Single source of monochromatic light
d
2 slits-separated by d
L
The rays start in phase, and travel the same distance, so they will arrive in phase.
Preflight 26.1
Screen a distance L from slits
Single source of monochromatic light
d
2 slits-separated by d
1) Constructive
2) Destructive
3) Depends on L
L
½ shift
The experiment is modified so that one of the waves has its phase shifted by ½ . Now, the interference will be:
Preflight 26.1
Screen a distance L from slits
Single source of monochromatic light
d
2 slits-separated by d
1) Constructive
2) Destructive
3) Depends on L
The rays start out of phase, and travel the same distance, so they will arrive out of phase.L
½ shift
The experiment is modified so that one of the waves has its phase shifted by ½ . Now, the interference will be:
Young’s Double Slit Concept
Screen a distance L from slits
Single source of monochromatic light
d
2 slits-separated by d
L
At points where the difference in path length is 0, ,2, …, the screen is bright. (constructive)
At points where the difference in path
length is
the screen is dark. (destructive)
2
5 ,
23 ,
2
Young’s Double Slit Key IdeaL
Two rays travel almost exactly the same distance. (screen must be very far away: L >> d)
Bottom ray travels a little further.
Key for interference is this small extra distance.
d
Path length difference =
d
Young’s Double Slit Quantitative
d sin
Constructive interference
Destructive interference
(Where m = 0, 1, 2, …)
sin(θ) tan(θ) = y/L
d
Path length difference =
d
Young’s Double Slit Quantitative
Destructive interference dsin (m
12)
Constructive interference dsin m
where m = 0, or 1, or 2, ...
d sin
Need < d
d
Destructive interference dsin (m
12)
Constructive interference dsin m
where m = 0, or 1, or 2, ...
Young’s Double Slit Quantitative
y
sin() tan() = y/L
dLm
y
d
Lmy
21
L
A little geometry…
d
L
Preflight 26.3
y
When this Young’s double slit experiment is placed under water. The separation y between minima and maxima
1) increases 2) same 3) decreases
d
L
Preflight 26.3
y
When this Young’s double slit experiment is placed under water. The separation y between minima and maxima
1) increases 2) same 3) decreases
…wavelength is shorter under water.
Preflight 26.2In the Young’s double slit experiment, is it possible to see interference maxima when the distance between slits is smaller than the wavelength of light?
1) Yes 2) No
Preflight 26.2In the Young double slit experiment, is it possible to see interference maxima when the distance between slits is smaller than the wavelength of light?
1) Yes 2) No
Need: d sin = m => sin = m d
If d then d > 1
so sin > 1
Not possible!
Reflections at Boundaries
Free End ReflectionNo phase change
Slow Mediumto
Fast Medium
Fast Mediumto
Slow Medium
Fixed End Reflection180o phase change
Newton’s Rings
Iridescence
Iridescence
Soap Film Interference• This soap film varies in
thickness and produces a rainbow of colors.
• The top part is so thin it looks black.
• All colors destructively interfere there.
Thin Film Interference
n1 (thin film)
n2
n0=1.0 (air)
t
1 2
Get two waves by reflection off of two different interfaces.
Ray 2 travels approximately 2t further than ray 1.
Reflection + Phase Shifts
n1
n2
Upon reflection from a boundary between two transparent materials, the phase of the reflected light may change.
• If n1 > n2
• If n1 < n2
Incident wave Reflected wave
Reflection + Phase Shifts
n1
n2
Upon reflection from a boundary between two transparent materials, the phase of the reflected light may change.
• If n1 > n2 - no phase change upon reflection.
• If n1 < n2 - phase change of 180º upon reflection. (equivalent to the wave shifting by /2.)
Incident wave Reflected wave
Thin Film Summary
n1 (thin film)
n2
n = 1.0 (air)
t
1 2
Ray 1: 1 = 0 or ½
Determine number of extra wavelengths for each ray.
If |(2 – 1)| = ½ , 1 ½, 2 ½ …. (m + ½) destructiveIf |(2 – 1)| = 0, 1, 2, 3 …. (m) constructive
Note: this is wavelength in film!
(film= o/n1)+ 2 t/ film
Reflection Distance
Ray 2: 2 = 0 or ½
This is important!
Thin Film Practice
nglass = 1.5
nwater= 1.3
n = 1.0 (air)
t
1 2
1 =
2 =
Blue light ( = 500 nm) incident on a glass (nglass = 1.5) cover slip (t = 167 nm) floating on top of water (nwater = 1.3).
Is the interference constructive or destructive or neither?
Phase shift = 2 – 1 =
Thin Film Practice
nglass = 1.5
nwater= 1.3
n = 1.0 (air)
t
1 2
1 = ½
2 = 0 + 2t / glass = 2t nglass/ 0= 1
Blue light ( = 500 nm) incident on a glass (nglass = 1.5) cover slip (t = 167 nm) floating on top of water (nwater = 1.3).
Is the interference constructive or destructive or neither?
Phase shift = 2 – 1 = ½ wavelength
Reflection at air-film interface only
Blue light = 500 nm incident on a thin film (t = 167 nm) of glass on top of plastic. The interference is:
1 2 3
44%
11%
44%nglass =1.5
nplastic=1.8
n=1 (air)
t
21
1. Constructive2. Destructive3. Neither
Blue light = 500 nm incident on a thin film (t = 167 nm) of glass on top of plastic. The interference is:
1 2 3
33%
11%
56%
nglass =1.5
nplastic=1.8
n=1 (air)
t
21
1. Constructive2. Destructive3. Neither
1 = ½ 2 = ½ + 2t / glass = ½ + 2t nglass/ 0= ½ + 1
Phase shift = 2 – 1 = 1 wavelength
Preflights 26.4, 26.5
The gas looks: • bright 67 %• dark 33 %
A thin film of gasoline (ngas=1.20) and a thin film of oil (noil=1.45) are floating on water (nwater=1.33). When the thickness of the two films is exactly one wavelength…
t =
nwater=1.3
ngas=1.20
nair=1.0
noil=1.45
The oil looks: • bright 35 %• dark 65 %
Preflights 26.4, 26.5
The gas looks: • bright• dark
A thin film of gasoline (ngas=1.20) and a thin film of oil (noil=1.45) are floating on water (nwater=1.33). When the thickness of the two films is exactly one wavelength…
t =
nwater=1.3
ngas=1.20
nair=1.0
noil=1.45
1,gas = ½
The oil looks: • bright• dark
2,gas = ½ + 2 1,oil = ½ 2,oil = 2|2,gas – 1,gas | = 2 | 2,oil – 1,oil | = 3/2
constructive destructive
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