Announcements 11/16/11
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Prayer
Labs 8, 9 due Saturday. Lab 10 due Tuesday.
We are nearing the homestretch for Optics… just
two lectures after today. (After that, relativity!)
We do have class Tuesday of next week
Exam 3 starts Monday after Thanksgiving break
Vote for review session, Mon/Tues/Wed next week
Pearls
Before
Swine
Reading Quiz
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A single slit diffraction pattern is characterized by:
a. A narrow central maximum, with other maxima
and minima on each side
b. A narrow central minimum, with other maxima
and minima on each side
c. A wide central maximum, with other maxima and
minima on each side
d. A wide central minimum, with other maxima and
minima on each side
Review: Interference from slits
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Quick writing: Using no equations, and in
hopefully no more than two sentences,
please explain the basic idea(s) behind
solving slit problems.
A “wide” slit (book: “narrow” slit)
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HW 34-3. How do we solve this?
“a” = width
of slit

  a sin 
Result: I ( )  I 0 sinc 
 

yscreen
approx.2: sin  
L



2
New function: sinc(x) 
 sin  x  
What is lim 

x0
x


sin  x 
x
The sinc function
[sinc(x)]2
sinc(x)
1.0
1.0
0.8
0.8
0.6
0.6
Image credit:
http://scripts.mit.edu/~tsg/
www/list.php?letter=Q
0.4
0.4
0.2
0.2
15
10
5
5
0.2
10
15
15
10
5
0
5
10
15
10
0
15
10
5
0.2
0.4
0.6
0.8
5
2
1.0

  a sin   
I ( )  I 0 sinc 





15
Single slit max/min
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Under what conditions will you get a min?
Under what conditions will you get a max?
What you need to know
Not given on exam
Given on exam
  2 PL 
PL  d sin 

E  E0 e
I~ E
i1
e
i2
y  L :   y L
 ...

2
two narrow slits:
2 d

I  I 0 cos 
sin  
  2

2
one wide slit:
2   a sin 
I  I 0sinc 





max : d sin   m


min : d sin   m  12 
min : a sin   m
Thought Question
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I shine light through two tiny slits spaced by
d. Then I shine the same light through a
single slit with width d. Which diffraction
pattern has the broadest middle peak?
a. The two slit pattern
b. The single slit pattern
c. Both middle peaks are the same size.
Image credit: Single slit
diffraction pictures from
Dr. Durfee
λ=5a
λ=a
λ = a/2
λ = a/3
λ = a/5
λ = a/10
51
01
5
0.1
8.0
6.0
4.0
2.0
0
5
01
51
Demo
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Diffraction from a slit
Diffraction from a hair (Babinet’s principle,
HW 34-2)
Reading Quiz
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When you have two slits close to each other,
each slit being “wide” (at least, not infinitely
narrow), the intensity you get on the screen is:
a. A double-slit pattern
b. A “wide” single-slit pattern
c. A double-slit pattern PLUS a single-slit
pattern
d. A double-slit pattern TIMES a single-slit
pattern
Combination of patterns
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mins
HW 34-4
max
max?
1.0
0.8
0.6
0.4
0.2
1.5
1.0
0.5
0.0
0.5
1.0
1.5
2-D patterns
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Pattern from x-direction  Pattern from y-direction
Example: rectangular aperture
zoomed in
x
y
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Thought question: Which dimension of the rectangle was the
narrowest?
a. X
b. Y
Circular Aperture (more on this next time)
Rectangle & Circle, side-by-side
Array of Circles
Thought Question
I shine light through a piece of foil
which has two identical holes shaped
like tiny llamas spaced apart by a
distance d. What will the diffraction
pattern look like?
A : The same as two narrow slits separated by d.
B : The same produced by a single slit of width d.
C : The diffraction pattern of a single llama.
D : The diffraction pattern of a single llama multiplied by the
two-slit pattern.
E : none of the above
Credit: All llama slides are from Dr. Durfee
Important: No llamas were harmed in the making of these images