Lec. 24, Thursday, April 8
Chapter 12: Wave Optics
We are here
Extra office hours TODAY: 4:30 – 5:30 pm
• Geometric optics compared to wave optics
• Phase
• Coherence
• Interference
• Huygens’ principle & diffraction
• Slits and gratings
• Diffraction patterns & spectra
• Thin films
Exam II: The average grade on exam II was 69.
An A is 82 or above, a B is 71 or better, a C is 59 or better.
Review of interference patterns
The pattern that two in phase speakers makes is shown below:
The speakers are displaced 2 ½ wavelengths vertically, so there is cancellation along a line in the vertical direction and there is addition in the horizontal direction. In the spaces between the loud areas the sound is softer.

Note that the lemon and lime triangles are similar.
The ratio of the shortest side to the longest side is the same for both.
So, the formula relating D, X, and
λ is
λ
/ X = S / D.
Wavelength of light:
λ
= S X / D. [measure all in the same units]
This is a slit
This a double slit
This is a grating
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Large hole, width >>
λ
, little diffraction
(Fresnel)
Very small spreading
Very slight fuzzy edges
Small hole, width <
λ
, “lots” of diffraction
(Fraunhofer) Distance from center to minimum (p. 334)
=
λ
D / b
D = distance to screen b = slit width
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Diffraction is spreading of rays.
Wavelength of light:
λ
= S X / D.
X = slit separation
D = screen distance
S = spot separation
S
Alternating light and dark lines are called fringes .
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Wavelength of light:
λ
= S X / D.
X = slit separation
D = screen distance
S = spot separation
S
This line is called
“second order”
Alternating light and dark lines are called fringes .
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The additional lines (higher orders) correspond to 1
λ
, 2
λ
, 3
λ
, etc. difference in the distances.
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Diffraction gives a spectrum if the incident light contains many wavelength
Wavelength of light:
λ
= S X / D.
X = slit separation
D = screen distance
S = spot separation
S
Alternating light and dark lines are called fringes .
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We are here
Lec. 24, Thursday, April 8
Chapter 12: Wave Optics
• Geometric optics compared to wave optics
• Phase
• Coherence
• Interference
• Huygens’ principle & diffraction
• Slits and gratings
• Diffraction patterns & spectra
• Thin films

A thin film of material can be an antireflection coating .
About 4% of light is reflected at the glass surface.
Reflections from surfaces of lenses create “ghost” images of the sun.
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Hard reflections return upside down
(180 degree phase change)
Examples
– wave on a rope tied to a wall
– light going into higher index of refraction material
– light reflecting from metal surface
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Demo this

Soft reflections return right side up
(No phase change)
Examples
– wave on a rope tied to a string
– light going into lower index of refraction material
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• Hard reflection: light goes from low index of refraction to high index, as air to glass.
The phase of the reflected wave is not changed.
• Soft reflection: light goes from high index to low (glass or water to air). The reflected wave is upside down (a 180 degree phase shift).
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• Each glass surface reflects about 4% of the incident light.
• Where the light enters, the reflection is hard .
• Where the light exits, the reflection is soft .
Fold this one over to get the reflected wave
Hard reflection
“fold over” the transmitted wave and turn it upside down
Soft reflection
Demo with thick plate air glass
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Enhanced reflection from a film 1
λ thick
The two reflected rays add in phase (brighter reflection) if the round trip in the film is two wavelengths,
Also for 1 wavelength round trip, etc.
Wavelengths are measured in the film, not in the air.
Indices of refraction are 1.0 for air, 1.3 for film, 1.5 for glass.
1
λ
Film Glass
Incident light
First reflection
(air to film)
Second reflection
(film to glass) 16

How did I know how to draw the reflected wave? The “hard” reflected wave is upside down, so if the incident wave is at a crest where it hits the film, then the reflected wave is at a trough where it starts on its backward path.
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The two reflected rays are out of phase (dimmer reflection) if the round trip in the coating is ½
λ
. Both reflections are hard. coating glass
Incident light
First reflection
(hard, air to film)
Second reflection
(hard, film to glass)
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Consider an antireflection coating on glass
¼
λ thick with index of refraction 1.3
Note that the two waves reflected cancel !
Each is turned upside down. One travels ½
λ further (round trip) than the other.
Thus the two reflected waves are out of phase and the reflection is “cancelled.”
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• ¼
λ film causes extra ½
λ round trip for light inside the film
• The wave reflected at the second surface is out of phase with wave reflected from the front if nothing else happens
• The front surface reflection is inverted (hard).
• The back surface reflection is inverted (hard)
• The front and back reflections are still out of phase.
• At ¾
λ film is also an antireflection coating.
• For an oil slick, the second reflection is soft and the reflected ray is inverted (something else happens).
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½ wavelength reflects less, ¼
λ reflects more.
Index of refraction for oil is 1.5, for water 1.3
oil water n=1.5 n = 1.3
0.5
λ
Incident light
First reflection
(hard, air to oil)
Second reflection
(soft, oil to water)
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Why do anti-reflection coatings look purple?
An anti-reflection coating is made ¼ wave thick for green light which is the middle of the spectrum. That means that blue and red are reflected a little bit because the film is optimized for green. The red and blue reflections together look purple.
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There is a “wedge” of air between the two lenses placed together.
Where the wedge is is ½
λ thick, the two reflected rays have paths different by 1
λ
, but one reflection is hard and one is soft, making the reflection darker since one reflected wave is inverted.
Demo: Newton’s rings, cash register tapes 23
Air to soapy water is a hard reflection.
Soapy water to air is a soft reflection.
Demo: soap film 24

Thin films create iridescent colors.
Peacock and hummingbird feathers: blue and cyan is from thin layers of cells.
Abalone shells and pearls: layers of calcium carbonate deposited in thin layers by the abalone or oyster.
Butterfly wings: thin layers of scales
Opal, a mineral, contains tiny particles regularly spaced which create colors by interference.
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