Announcements 11/9/12
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Prayer
Clement sick today, no office hours
Lab 8 going on, due on Sat Nov 17
Lab 9 starts tomorrow, due on
Sat Nov 17
Lab 10 starts tomorrow, due on
Tues Nov 20
Exam 3 starts day after break
Two facts you should know:
eix  eix
cos x 
2
eix  eix
sin x 
2i
(They follow quickly from
eix = cosx + i sinx)
From warmup
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Extra time on?
a. (nothing in particular)
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Other comments?
a. (nothing in particular)
Double slit diffraction
Two slit interference
From Wikipedia
http://en.wikipedia.org/wiki/
Double-slit_experiment
From warmup
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What is the purpose of S1 in the right figure? Some good thoughts:
a. To make sure that the light sources at b and c are identical
b. Is it to make sure that the point source of light is centered
exactly between b and c and to make sure that b and c are
coherent?
c. That is the original ray. The two slits b and c split it up like a
speaker splits up a single sound wave.
Reminder: How did we do it with sound?
An alternate method: Use a laser, then S1 not needed
Double slit experiment
aka “Young’s Double Slit”
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Essentially the same
as the two speaker
demo
min
max
min
Goal: what’s the
shape of that curve?
How can we predict
where the maxima
& minima will be?
screen
here
intensity
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max
Wait, which is correct?
The Easy Part
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Maxima/minima
Approximation #1: d is small
enough that the two rays are
parallel. Requires d << L.
Maxima: DPL = ?
d sin   m
Minima: DPL = ?
d sin   m  12 
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From warmup
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Consider a two-slit interference pattern like those above.
What do you suppose would happen if the entire setup
were immersed in water?
a. The bars would move together and get smaller because
the wavelength decreases when you immerse it in
water, therefore the distance between the bars is
decreased.
How to solve the problem
Complex numbers!!
 The light from each slit travels a different distance
a. This creates a phase shift
b. Incorporate the phase shift into eif factors
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First: what’s the phase shift for two waves
oscillating in phase with a known DPL?
Quick writing (w/o Approx. 1)
3.2 m
two sources
of sound, =1.2m
(in phase)
what is relative
phase shift, here?
3.0 m
f = ( DPL /  )  360
f = 2pDPL / 
f ( x, t )  A cos(kx  t )  A cos(kx  t  60 )
How to add?
Intensity?
What’s DPL?
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Clicker Vote: What should
we measure the phase
shift relative to?
a. The top slit
b. The bottom slit
c. Halfway between the
two slits
f = 2pDPL / 
The Full Answer
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Etot = Etop slit + Ebottom slit
= [use whiteboard]
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I ~ |E|2
I = [use whiteboard]
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Plot of I(y) for I0=1, =500 nm, L=1 m, d=1 mm
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How did I turn  into y?
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Approximation #2: sometimes (not here!)  is small
enough that   y/L. Requires y << L.
f = 2pDPL / 
 2p d

I  I 0 cos2 
sin  
  2
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Plots
2p d

I  I 0 cos 
sin  
  2
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2
  tan
1
 y / L
(approx. 1 only)
2  p dy

I  I 0 cos 


L
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(approx. 1 and 2)
min
max
min
screen
here
intensity
max
max
min
max
min
max
min
max
screen
here
Maxima/minima, revisited
2p d

I  I 0 cos 
sin  
  2

2
2  p dy

I  I 0 cos 

 L 
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Max: cosx = 1  …
d sin   m
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Min: cosx = 0  …
d sin   (m  12 )
What you need to know
Not given on exam
Given on exam
f  2p DPL 
DPL  d sin  (approx. #1)
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E  E0 eif1  eif2  ...
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d sin   m
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d sin   m  12 
  y L (approx. #2)
2
Demo: Double
I~ E
2  p dy 
I  I 0 cos 
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2  2p d slit experiment!

I  I cos
sin 
L
0
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  2
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HW 32-4: Solve the three slit problem
Exam problem likely (possibly extra credit)
Disclaimer: This only works for very narrow slits
 Lecture after next: “wide” slits
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