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12/10/05 U. Wisconsin, Physics 104, Fall 2003 1
Interference & Diffraction
• Review of Interference
• Diffraction
12/10/05 U. Wisconsin, Physics 104, Fall 2003 2
Preflight 1
All 3 rays are interfering constructively
at the point shown.
If the intensity from ray 1 is Io , what is
the combined intensity of all 3 rays?
16%
66%
18%
0% 20% 40% 60% 80%
E field is 3 times the amplitude B field is 3 times the amplitude Both are in phase - I=EB is 9 times!
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Preflight 2
Now consider the same three slits as
in the previous question, but
suppose the angle is such that rays 1
and 2 are interfering destructively.
Is the intensity from the three rays a
minimum?
48%
52%
0% 20% 40% 60% 12/10/05 U. Wisconsin, Physics 104, Fall 2003 4
Huygen’s Principle
Bending around corners
Bending around corners
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Single Slit Interference?!
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Wall
Screen with opening (or obstacle without screen)
shadow
bright
Diffraction Rays
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Diffraction/ Huygens
Every point on a wave front acts as a source of tiny wavelets that move forward. JAVA
We see maxima and minima on the wall.
Light waves originating at different points within opening travel different distances to wall, and can interfere!
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1 st^ minima
Central maximum
D
Rays 2 and 2 also startD/2 apart and have the same path length difference.
1 st^ minimum at sin = /D
Condition for every ray originating in top half of slit to interfere destructively with the corresponding ray originating in bottom half.
Diffraction: Interference of light from
within just one slit
D 2
D 2 sin^ ^
When rays 1 and 1 will interfere destructively.
D 2
sin =^ 2
D
Rays 2 and 2 also startD/4 apart and have the same path length difference.
Condition for every ray originating in top half of slit to interfere destructively with the corresponding ray originating in bottom half. 2nd^ minimum at sin = 2 /D
Diffraction: Interference of light from
within just one slit
D 4
D 4
sin
When rays 1 and 1 will interfere destructively.
D 4
sin =^ 2
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These objects arejust resolved Two objects are just resolved when the maximum from one is at the minimum of the other. 12/10/05 U. Wisconsin, Physics 104, Fall 2003 20
Two objects are just resolved when the maximum from one is at the minimum of the other.
sin min min = 1.
D
min
To see two objects distinctly,
need min
Resolving Power
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Preflight 6
Astronaut Joe is standing on a distant planet with binary suns. He wants to see them but knows it’s dangerous to look straight at them. So he decides to build a pinhole camera by poking a hole in a card. Light from both suns shines through the hole onto a second card. But when the camera is built, Astronaut Joe can only see one spot on the second card! To see the two suns clearly, should he make the pinhole larger or smaller?
54%
0% 20% 40% 60% 12/10/05 U. Wisconsin, Physics 104, Fall 2003 22
sin min min = 1.
D
Resolving Power Question
How does the maximum resolving power of your eye change when the brightness of the room is decreased.
- Increases 2) Constant 3) Decreases
When the light is low, your pupil dilates (D can increase by factor of 10!)
Recap
- Huygens’ Principle: Each point on wave front acts
as coherent source and can interfere.
- Interference: Coherent waves
- Full wavelength difference = Constructive
- _ wavelength difference = Destructive
- Multiple Slits (2 or more slits with separation d)
- Constructive d sin() = m (m=1,2,3…)
- More slits = brighter max, darker mins
- Single Slit:
- Destructive: D sin() = m (m=1,2,3…)
- Resolution: Max from 1 at Min from 2
Polarization
Orientation of the field vectors
Changes due to reflection,
medium properties, scattering,…
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z^ x
y
E
B
Only the loop in the xy plane will have a magnetic flux through it as the wave passes. The flux will oscillate with time and induce an emf.
loop in xy plane
loop in xz plane loop in yz plane 1 2 3
Which orientation will have the largest induced emf. Hint: Use Faraday’s law
31%
45%
24%
0% 10% 20% 30% 40% 50%
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Polarization
Orientation of E field matters when
the EM wave traverses matter
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Polarization
• Transverse waves have a polarization
- (Direction of oscillation of E field for light)
• Types of Polarization
- Linear (Direction of E is constant)
- Circular (Direction of E rotates with time) **
- Unpolarized (Direction of E changes randomly)
x z
y
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Natural Light is Unpolarized
• Light from sun
• We can polarize light using special material
• Crystals, Polymers with aligned atoms …
Linear Polarizers
• Linear Polarizers absorb all electric fields
perpendicular to their transmission axis.
Molecular View
Unpolarized Light on
Linear Polarizer
- Most light comes from electrons accelerating in random directions and is unpolarized.
- Averaging over all directions, intensity of transmitted light reduces due to reduction in E (^) I = c^ 0 E^^2
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Polarization by Reflection
• Light can by polarized by reflection
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Preflight 12
- Unpolarized light traveling in air is incident on a glass block. Which of the following statements about it is true: - Only reflected light is partially polarized. - Only refracted light is partially polarized. - Both reflected and refracted light is partially polarized - Both reflected and refracted light are unpolarized
8%
34%
41%
17%
0% 10% 20% 30% 40% 50%
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Preflight 13
- Is it possible for the reflected ray to be fully polarized?: - Yes - No
50%
50%
0% 10% 20% 30% 40% 50%
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Brewster’s angle
• Partially polarization on
reflection
• Part of the light is refracted
(also polarized)
• Depends on refractive indices
- Brewster’s law Complete polarization for Brewster's angle tan b = n n^2 1 Light from medium with n 1 reflects off from n 2 In your text n 1 = 1 (~ air) was chosen
Preflight 14
- Unpolarized light traveling in air is incident on a glass block. The Brewster angle is 56 o^ for this situation. If the glass block is placed in water, the reflected light in water will be have a Brewster angle that is: - greater. - the same. - lower 21%
43%
37%
0% 10% 20% 30% 40% 50% Brewster's angle tan b = n n^2 1 n 1 has increased from 1 to 1. tan b decreases Do Problem 24.
Preflight 10
- Polarized glasses are considered as better than normal glasses because: - They block more light - They are safer for your eye - They decrease glare - They are cheaper 11%
37%
22%
30%
0% 10% 20% 30% 40%
Reflected light is polarized - polarizing glass cuts out a fraction of that light increasing clarity of vision.
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Preflight 11
- Polaroid sun glasses absorb light that is polarized in what direction?: - Horizontal - Vertical
46%
54%
0% 20% 40% 60%
Reflected light is polarized - polarizing glass cuts out electric field perpendicular to the transmission axis. To cut out the glare, (e.g., reflections off snow on the ground, … coming horizontally) glasses are aligned with transmission axis vertical to cut of horizontal light. 12/10/05 U. Wisconsin, Physics 104, Fall 2003 44
Polarization by Scattering
- Light can also be polarized in scattering processes - Light scatters of molecules in air - Rotate polarized sunglasses while looking at blue sky - Light gets cut off - blue sky turns brighter and dimmer as you rotate indicating polarization
Controlled Polarization
- Electrical voltage on a liquid crystal diode - Turns on and off polarizing filter effect - Used in LCD display
Optically Active Materials
Birefringence
splits into two
