Announcements 11/11/11
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Prayer
Lab 8 going on, due on Sat Nov 19
Lab 9 starts tomorrow, due on Sat Nov 19
Lab 10 starts tomorrow, due on Tues Nov 22
Slinky (down to you, Thomas…)
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)
Reading Quiz
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According to the book, a double-slit diffraction pattern (viewed on
a screen far from the slits) is:
a. A series of equal amplitude peaks, equally spaced
b. A series of equal amplitude peaks, alternating between two
spacing distances
c. A series of alternating amplitude peaks, equally spaced
d. A series of alternating amplitude peaks, alternating between
two spacing distances
Two slit interference
From Wikipedia
http://en.wikipedia.org/wiki/
Double-slit_experiment
Double slit experiment
aka “Young’s Double Slit”
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Exactly 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

max
Experimental challenge
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How do you get two points sources of light that are
oscillating in phase with each other?
Wait, which is correct?
a. How did we do it with sound?
b. Options for light? (I can only think of two)
c. What he did:
http://en.wikipedia.org/wiki/
Young's_Double_Slit_Interferometer
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
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First: what’s the phase shift for two waves
oscillating in phase with a known DPL?
f = ( DPL / l )  360
f = 2pDPL / l
What’s DPL?
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Clicker Vote: What should
we measure the path
length relative to?
a. The top slit
b. The bottom slit
c. Halfway between the
two slits
f = 2pDPL / l
Approximation #1: d is small
enough that the two rays are
parallel. Requires d << L.
The Easy Part
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Maxima/minima
Maxima: DPL = ?
d sin   ml
Minima: DPL = ?
d sin   m  12 l
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
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, l=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 / l
 2p d

I  I 0 cos2 
sin  
 l 2

Plots
2p d

I  I 0 cos 
sin  
 l 2

2
  tan
1
 y / L
(approx. 1 only)
2  p dy

I  I 0 cos 

l
L


(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  
 l 2

2
2  p dy

I  I 0 cos 

 lL 
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Max: cosx = 1  …
d sin   ml
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Min: cosx = 0  …
d sin   (m  12 )l
What you need to know
Not given on exam
Given on exam
f  2p DPL l
DPL  d sin  (approx. #1)
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E  E0 eif1  eif2  ...
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d sin   ml
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d sin   m  12 l
  y L (approx. #2)
2
Demo: Double
I~ E
2  p dy 
I  I 0 cos 

2  2p d slit experiment!

I  I cos
sin 
lL
0
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 l 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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