Announcements 11/14/12
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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: Intro to
Relativity
Exam 3 starts Monday after
Thanksgiving break
Vote for review session,
Mon/Tues/Wed next week
Speed
Bump
From warmup
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Extra time on?
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Other comments?
From warmup:
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As shown below, the
diffraction pattern of a single
slit has a broad maximum in
the middle, then narrower
maxima to the sides. How
does the intensity of the
broad middle peak compare
to the intensity of the closest
side peaks?
a.
b.
c.
d.
e.
Broad peak is a lot more
intense (~21x)
Broad peak is a little more
intense
Same intensity
Side peaks are a lot more
intense
Side peaks are a little more
intense
From warmup:
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This is the diffraction
pattern for a single wide
slit. What will happen to the
pattern if the slit is made
narrower? (The bottom
physical pattern not the top
mathematical plot.)
a. If the slit is made
narrower ("a"
decreases), then the
spacing between minima
and maxima will
increase. That is, the
pattern will spread out.
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
Clicker 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)
Clicker question:
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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
From warmup
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This is the diffraction pattern for two
wide slits. (a) What will happen here
if the distance between slits is made
narrower? (b) What is the distance is
held constant but the width of each
slit is made narrower.
a. (a) If the distance between slits
is made narrower, the "fringes"
(high frequency oscillation) will
spread out, but the "diffraction
minima" (low frequency
oscillation) will stay in the same
places.
b. (b) If the width of each slit is
made narrower, the diffraction
minima will spread out but the
interference fringes will stay in
the same places.
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
Clicker 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