Announcements 11/16/12 Prayer Labs 8, 9 due tomorrow  anyone still have issues with interferometer? Lab 10 due Tuesday Exam 3 starts Monday after break Exam 3 review session: Mon after break 4:30-6 pm, room ??? (I’ll tell you on Monday) Dilbert

From warmup (last time & this time) Extra time on? a. a.Holograms (2 students) b. b.Yes, I don't understand how there is light in the middle of the shadow of a penny in the example the book gave, does the penny have a small hole in the middle of it? – – “Poisson spot”, aka “Arago spot”, predicted by Fresnel in 1818 Other comments? a. a.You know what would be just really great? Honors credit! I'm sure it's impossible at this point, but don't you think a harder class deserves more credit? b. b.At the review session, can you give us a review of all things having to do with slits, equipping us with tools with which we can solve any slit problem that comes our way? c. c.What is the best preparation for the final?

Clicker question: What does Rayleigh’s criterion tell us? a. a.The angle at which both light polarizations have equal reflection coefficients b. b.The angle at which p-polarized light has minimum reflection c. c.The angular separation resolvable by an imaging system d. d.The number of orders produced by a diffraction grating

Suppose you are trying to resolve a binary star system with a telescope. Can you improve the resolving power (increase the resolution) using a color filter? Explain. a. a.Wrong answers: index of refraction of air, anything to do with atmosphere, interference between colors, etc. b. b.Right answer: Since a color-filter only lets in light of its color, or wavelength, it would be best to find a color filter that allows the lowest wavelength through, therefore lowering theta_min. From warmup

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? pattern at infinity pattern at focus superimposed patterns at focus f board with hole

Rayleigh: 2 nd peak at position of first minimum

Rayleigh Criterion plotted vs (  D/ ) Mathematica “FindRoot” command:  D/ = … (using sin    ) Shape of curve involves a “Bessel function” Rayleigh Criterion

Cat's eyes have pupils that can be modeled as vertical slits. At night would cats be more successful resolving the headlights of a far away car if the car is horizontal (regular) or tilted vertically? Explain. a. a.Vertically because then D would be greater and so the minimum angle would be smaller. b. b.The cat would be better at resolving it if the car was tilted vertically. However, it would be worse for the car. From warmup

3 slits, equally spaced Back to 1-D slits, infinitely narrow (created with parameters so period = 2  )

4 slits, equally spaced Back to 1-D slits, infinitely narrow

5 slits, equally spaced Back to 1-D slits, infinitely narrow

10 slits, equally spaced Back to 1-D slits, infinitely narrow

20 slits, equally spaced Back to 1-D slits, infinitely narrow

100 slits, equally spaced Back to 1-D slits, infinitely narrow What have we learned?

The Grating Equation Where will maxima be?

Resolving Power N=100 Goes to zero at x= = 2  /100 width = 1/N  separation of maxima

Resolving Power Red light vs. Green light HW 35-6(c): resolving power = /  = N  m

Demos Circular aperture Diffraction grating … with two lasers … with white light source

Clicker question: Diffraction of x-rays off of planes of atoms in a crystal is governed by whose law? a. a.Bragg’s Law b. b.Bohr’s Law c. c.Compton’s Law d. d.Raman’s Law e. e.Thompson’s Law

X-ray Diffraction by Crystals Bragg equation wiki/File:Bragg_diffraction.png fisica.bo.imm.cnr.it/english/history/figuredett2.html 2dsin  = m (constructive)

Laue Patterns