Announcements 3/25/11
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Prayer
One lab due Saturday, two new labs start on
Saturday.
We are nearing the homestretch for Optics… just
two lectures after today. (After that, relativity!)
Exam 3 starts a week from tomorrow
a. Review session next Thurs or Friday. I sent
survey link. I will schedule the room on Monday
morning, so please select your favorite times
before then.
Reading Quiz
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Which of the following can generate a
diffraction or interference pattern?
a. Light passing through a pinhole in a card
b. Light passing through an array of regularly
spaced pinholes
c. Light clipped by the edge of a razor blade
d. Both A and B
e. All of the above
Review: Interference from slits
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Quick writing: Using no equations, and in
hopefully no more than two sentences,
please explain how to solve slit problems.
A “wide” slit (book: “narrow” slits)
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HW 34-3. How do we solve this?
“a” = width
of slit

  a sin 
Result: I ( )  I 0 sinc 
 

y
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 max?
Under what conditions will you get a min?
What you need to know
2   a sin 
I ( )  I 0sinc 

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



2   ay

I ( )  I 0sinc 

 L 
What sincx and sinc2x look like
The two formulas above (on notecard, unless
you can quickly derive them)
How to do the integral (HW 34-3)
Conditions for max/min (on notecard, unless you
can quickly derive them)
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.
d. Masspacity  Not the answer!!
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
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