Announcements 3/28/12 Prayer Exam review problems for sign-up

Calvin & Hobbes

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

Lenses

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:

Lens Fourier Transforms

From Hecht

at focus of lens

“Fourier Transform smoothing”

From Hecht

Before After

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

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.

Simple Telescope

Circular Aperture, again

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

Rayleigh: 2nd peak at position of first minimum

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))