announcements 11/14/12
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Announcements 11/14/12. Speed Bump. 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 - PowerPoint PPT PresentationTRANSCRIPT
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Announcements 11/14/12 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
SpeedBump
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From warmup Extra time on?
Other comments?
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From warmup: 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. Broad peak is a lot more intense (~21x)
b. Broad peak is a little more intense
c. Same intensityd. Side peaks are a lot more
intensee. Side peaks are a little more
intense
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From warmup: 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.
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Review: Interference from slits Quick writing: Using no equations, and
in hopefully no more than two sentences, please explain the basic idea(s) behind solving slit problems.
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A “wide” slit (book: “narrow” slit) HW 34-3. How do we solve this?
Result: 2
0sin( ) sinc aI I
approx.2: sin screenyL
sinsinc( )
xx
xNew function:
What is
0
sinlimx
xx
“a” = width of slit
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The sinc function
sinc(x) [sinc(x)]2
15 10 5 5 10 15 0.2
0.2
0.4
0.6
0.8
1.0
15 10 5 0 5 10 15
0.2
0.4
0.6
0.8
1.0
Image credit: http://scripts.mit.edu/~tsg/www/list.php?letter=Q
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Single slit max/min
Under what conditions will you get a min?
Under what conditions will you get a max?
2
0sin( ) sinc aI I
1
5
10
5
05
10
15
0.2
0.4
0.6
0.8
1.0
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What you need to know
20
2cos sin2dI I
Given on exam Not given on exam
max : sind m
12min : sind m
2 PL :y L y L PL sind
1 20 ...i iE E e e 2~I E
20
sinsinc aI I
two narrow slits:
one wide slit:min : sina m
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Clicker question: 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 patternb. The single slit patternc. Both middle peaks are the same size.
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λλ = 5 = 5 aaImage credit: Single slit diffraction pictures from Dr. Durfee
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λλ = = aa
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λλ = = aa/2/2
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λλ = = aa/3/3
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λλ = = aa/5/5
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λλ = = aa/10/10
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Demo Diffraction from a slit Diffraction from a hair (Babinet’s
principle, HW 34-2)
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Clicker question: 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 patternb. A “wide” single-slit patternc. A double-slit pattern PLUS a single-slit
patternd. A double-slit pattern TIMES a single-slit
pattern
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From warmup 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.
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1.5 1.0 0.5 0.0 0.5 1.0 1.5
0.20.40.60.81.0
Combination of patterns HW 34-4 maxmins max?
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2-D patterns Pattern from x-direction Pattern from y-direction
Thought question: Which dimension of the rectangle was the narrowest?
a. Xb. Y
Example: rectangular aperture zoomed in
xy
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Circular Aperture (more on this next time)
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Rectangle & Circle, side-by-side
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Array of Circles
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Clicker question:I shine light through a piece of foil I shine light through a piece of foil which has two identical holes shapedwhich has two identical holes shapedlike tiny llamas spaced apart by a like tiny llamas spaced apart by a distance distance dd. What will the diffraction . What will the diffraction pattern look like?pattern look like?
A : The same as two narrow slits separated by A : The same as two narrow slits separated by dd..B : The same produced by a single slit of width B : The same produced by a single slit of width dd..C : The diffraction pattern of a single llama.C : The diffraction pattern of a single llama.D : The diffraction pattern of a single llama multiplied D : The diffraction pattern of a single llama multiplied
by the two-slit pattern.by the two-slit pattern.E : none of the aboveE : none of the above
Credit: All llama slides are from Dr. Durfee
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Important: No llamas were harmed in the making of these images