1. Announcements 3/23/11 Prayer Two labs this week (telescope, interferometer) Review:

2. Fourier Transforms? From last time: what did our two-slit analysis have 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  1 ! (Could have an overall reference phase…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 wave on a string moves from a fast velocity section to a slow velocity section, the reflected wave is phase-shifted by 180 . When a wave moves from a slow section to a fast section, however, the reflected wave has no phase shift. How does the phase shift of a light wave moving from one medium to another compare to that? (close to normal incidence) a. a.The phase shift obeys the same rules b. b.The phase shift is the same for fast-to-slow, but reversed for slow-to-fast c. c.The phase shift is the same for slow-to-fast, but reversed for fast-to-slow d. d.The phase shift is reversed for both cases

9. Remember these? “Fresnel Equations” If near perpendicular (1-D problem) For arbitrary angle Just the 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. Back to 1D case 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 What changes if rays really are at an angle?

11. 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)

12. 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

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

14. Demo Demo: Soap film

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