Announcements 3/21/11
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Prayer
Two labs this week (telescope, interferometer)
Two mathematical facts you should know:
e e
cos x 
2
ix
ix
e e
sin x 
2i
ix
ix
(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) looks like:
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
Interference...
A single source
Interference...
Two sources
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?
a. How did we do it with sound?
b. Options for light? (I can only think of two)
c. What he did:
Image credit: Wikipedia
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 Answer
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Etot = Etop slit + Ebottom slit
=…
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I ~ |E|2
I=…
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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 q into y?
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Approximation #2: q is small enough that qy/L.
Requires y << L.
f = 2pDPL / l
Plots
2p d

I  I 0 cos 
sin q 
 l 2

2
q  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
How to predict max/min
2p d

I  I 0 cos 
sin q 
 l 2

2
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Max: cosx = 1  …
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Min: cosx = 0  …
2  p dy

I  I 0 cos 

 lL 
d sinqbright  ml
d sinqdark  (m  12 )l
What you need to know
2  p dy 

2  2p d
I  I 0 cos 
I  I 0 cos 
sin q 

 lL 
 l 2

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How to solve the problem this way—works for any
number/pattern of slits
a. You analyze three slits for HW 32-4
b. Could be problem like this on exam
This only works for very narrow slits (width <<
separation between slits)
The two formulas above (on notecard, unless you can
quickly derive them)
Conditions for max/min (on notecard, unless you can
quickly derive them)
Wrapping Up
2p d

I  I 0 cos 
sin q 
 l 2

2
max :
d
l
sin q  m
d
1
min : sin q  m 
l
2
The fast way to get these
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Demo: Double-slit experiment
2  p dy

I  I 0 cos 

 lL 
dy
max :
m
lL
dy
1
min :
 m
lL
2