1. Announcements 11/14/11 Prayer HW 29 problem Labs 8 & 9 due Saturday Progress Reports… Review: Rubes

2. Fourier Transforms? How can our two-slit analysis possibly have anything to do with Fourier transforms? (this is the y-coordinate on the slits, not the y-coordinate on the screen) compare to:

3. Adding up phases … For an equally-spaced pattern of slits, how do the  PLs compare? Each  is a multiple of  2 ! (Could have an overall reference phase for  1 …not too important.) slits screen In short, we need to add up a bunch of vectors that have the same magnitude (1), but angles (phases) that go like 0 , 20 , 40 , 60 , etc. For a different position on the screen (measured by y or , we need to add up a different set of phases… perhaps like 0 , 21 , 42 , 63 , etc.

4. Adding up phases, cont. … Quick writing: graphically add these three vectors: 1  0  + 1  20  + 1  40  What about 1  0  + 1  90  + 1  180  slits screen

5. Three Slit Problem: Scanning Theta Credit: this animation and the next one are from Dr. Durfee Note: for some reason he picked the overall reference phase to be about 20 

6. Thought question How many “sub” peaks are there between the “main” peaks in a 5-slit interference pattern? a. a.1 b. b.2 c. c.3 d. d.4 e. e.5

7. Five Slit Problem: Scanning Theta Note: for some reason he picked the overall reference phase to be about 20-30 

8. Reading Quiz When a light wave travels from a low index to a high index material at normal incidence (perpendicular to surface), what is the phase shift of the reflected wave? a. a.0  b. b.45  c. c.90  d. d.180  e. e.depends on whether it is s- or p-polarization

9. Remember these? “Fresnel Equations” If near perpendicular (1-D problem) For arbitrary angle Same as strings The Truth (overlooked by textbook): you don’t always get a phase shift, even if going fast to slow. (Brewster marks boundary) More Truth: sometimes phase shifts not just 180  : can have complex n, complex , etc. You can’t handle this much truth!

10. Air to glass (n=1 to n=1.5) p-polarization r t field amplitudes vs  Brewster 180  phase shift (close to perpendicular) 0  phase shift (close to glancing)

11. Back to “near normal incidence” Rays drawn at an angle to make viewing easier. They’re really perpendicular to surface. From low to high index: 180  phase shift From high to low index: no phase shift What does the thickness of this slab need to be to get constructive interference between the two rays? air thin glass thickness t If rays at an angle… determine if above/ below Brewster angle (if p-polarization).

12. Optical path length OPL = Path Length  n  since wavelength inside the material is reduced by a factor of n, the distance “looks” bigger than it actually is Constructive interference:  OPL (  any phase shifts) = m Destructive interference:  OPL (  any phase shifts) = (m+1/2)

13. New situation Rays drawn at an angle to make viewing easier. They’re really perpendicular to surface. What does the thickness of the COATING need to be to get constructive interference between the two rays? air thick glass, n = 1.5 thin coating, n = 1.3 thickness t

14. Pretty pictures What’s going on here? http://twilit.wordpress.com/2008/ 03/15/bubbles-and-interference/ http://superphysics.netfirms. com/pp_optics.html

15. Demo Demo: Soap film

16. Interferometer From lab 9: Interference! How does this disprove the ether? changing optical path length, yields n gas