Announcements 3/28/12
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Transcript of Announcements 3/28/12
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Announcements 3/28/12 Prayer Exam review problems for sign-up
Calvin & Hobbes
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Reading Quiz A lens placed after a diffraction aperture
causes the Fraunhofer pattern to be produced:
a. before the focal lengthb. at the focal lengthc. after the focal length (but at a finite
distance)d. at infinity
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Lenses
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Lenses What it object is not at infinity?
a. What appears at q?b. What appears at f?
“Fourier transform plane”
f f f f
Object at f:
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Lens Fourier Transforms
From Hecht
at focus of lens
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“Fourier Transform smoothing”
From Hecht
Before After
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Reading Quiz
What does the “Rayleigh criterion” tell us?a. The angle at which both light
polarizations have equal reflection coefficients
b. The angle at which p-polarized light has minimum reflection
c. The angular separation resolvable by an imaging system
d. The number of orders produced by a diffraction grating
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Reading Quiz The Rayleigh criterion for resolving two
point light sources comes from:a. Fourier transforms of delta functions.b. Jinc functions’ maxima and minima. c. Lagrange multipliers.d. Parallax of stars.
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Simple Telescope
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Circular Aperture, again
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What do you get in this situation?
What if there’s a lens in the hole?
What if there isn’t a board?
What if you have two light sources?
patt
ern
at in
finity
patt
ern
at f
ocus
supe
rimpo
sed
patt
erns
at
focu
s
f
board with hole
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Rayleigh: 2nd peak at position of first minimum
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Rayleigh Criterion
plotted vs (krb/f), = D/
Mathematica “FindRoot” command: / = 1.21967…
min.resolve 1.22D
(using sin )
Curve is (J1(x)/x)2
Rayleigh Criterion
(= first zero of J1(x))