Light Interference Continued

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Light Interference Continued
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Superposition
Constructive Interference

In Phase
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Superposition
Destructive Interference
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t
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Out of Phase 180 degrees
t
-1
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Superposition

Different f
1) Constructive 2) Destructive 3) Neither
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Interference Requirements

• Need two (or more) waves
• Must have same frequency
• Must be coherent (i.e. waves must have definite
  phase relation)

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Interference for Sound
For example, a pair of speakers, driven in phase,
producing a tone of a single f and l
But this wont work for light--cant get coherent
sources
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Observe Laser Light Through

• One Slit
• Two Slits
• Multiple Slits

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Observe Laser Light Through

• One Slit Broad Central Maximum
• Two Slits Central Bright Spot with
• symmetric dark fringes.
• Multiple Slits Central Bright Spot. Narrowor
• bright spots, brighter maximums, darker
• minimums.

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Single Slit Diffraction
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Double Slit
Interference Only
Interference Diffraction
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Five Slit Diffraction Grating (Inteference
Diffraction)
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• How do we predict the locations of the bright and
  dark fringes produced by a single slit? double
  slit? Multiple slit?

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Youngs Double Slit 1
Light waves from a single source travel through 2
slits before meeting on a screen. The
interference will be

1. Constructive
2. Destructive
3. Depends on L

d
The rays start in phase, and travel the same
distance, so they will arrive in phase.
Single source of monochromatic light ?
L
2 slits-separated by d
Screen a distance L from slits
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Young Double Slit 2
The experiment is modified so that one of the
waves has its phase shifted by ½ l. Now, the
interference will be

1. Constructive
2. Destructive
3. Depends on L

d
The rays start out of phase, and travel the same
distance, so they will arrive out of phase.
Single source of monochromatic light ?
L
2 slits-separated by d
Screen a distance L from slits
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Youngs Double Slit Concept
At points where the difference in path length is
0, l,2l, , the screen is bright. (constructive)
d
Single source of monochromatic light ?
L
Screen a distance L from slits
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Youngs Double Slit Key Idea
L
Two rays travel almost exactly the same
distance. (screen must be very far away L gtgt d)
Bottom ray travels a little further. Key for
interference is this small extra distance.
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Youngs Double Slit Quantitative
d
d
Path length difference
d sin q
Need l lt d
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Youngs Double Slit Quantitative
L
d
A little geometry
sin(q) ? tan(q) y/L
Constructive interference
Destructive interference
where m 0, or 1, or 2, ...
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Youngs Double Slit 3
L
y
d
When this Youngs double slit experiment is
placed under water. The separation y between
minima and maxima 1) increases 2) same 3)
decreases
Under water l decreases so y decreases
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Double Slit 4
L
d
d sinq
Path length difference
d sin(?)
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Multiple Slits (Diffraction Grating N slits
with spacing d)
L
d
l
d sinq
Path length difference 1-2
2l
3l
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Diffraction Grating
N slits with spacing d
q
screen VERY far away
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Three slit interference
9I0
I0
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Multiple Slit Interference (Diffraction Grating)
Peak location depends on wavelength!
Region between maxima gets suppressed more and
more as no. of slits increases bright fringes
become narrower and brighter.
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Single Slit Interference?!
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Diffraction Rays
This is not what is actually seen!
Screen with opening (or obstacle without screen)
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Diffraction/ Huygens
Every point on a wave front acts as a source of
tiny wavelets that move forward.

Light waves originating at different points
within opening travel different distances to
wall, and can interfere!

We will see maxima and minima on the wall.
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Single Slit Diffraction
W
Rays 2 and 2? also start W/2 apart and have the
same path length difference.
Under this condition, every ray originating in
top half of slit interferes destructively with
the corresponding ray originating in bottom half.
1st minimum at sin q l/w
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Single Slit Diffraction
w
Rays 2 and 2? also start w/4 apart and have the
same path length difference.
Under this condition, every ray originating in
top quarter of slit interferes destructively with
the corresponding ray originating in second
quarter.
2nd minimum at sin q 2l/w
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Single Slit Diffraction Summary
Condition for halves of slit to destructively
interfere
Condition for quarters of slit to destructively
interfere
Condition for sixths of slit to destructively
interfere
All together
THIS FORMULA LOCATES MINIMA!!
Narrower slit gt broader pattern
Note interference only occurs when w gt l
l
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Recap.

• Interference Coherent waves
• Full wavelength difference Constructive
• ½ wavelength difference Destructive
• Multiple Slits
• Constructive d sin(q) m l (m1,2,3)
• Destructive d sin(q) (m 1/2) l 2 slit only
• More slits brighter max, darker mins
• Huygens Principle Each point on wave front acts
  as coherent source and can interfere.
• Single Slit
• Destructive w sin(q) m l (m1,2,3)
• Resolution Max from 1 at Min from 2

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