Announcements 11/12/10

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Announcements 11/12/10  Prayer  Two labs this week (telescope, interferometer)  The missing exams…  Project progress reports: I’m about 75% of…
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Announcements 11/12/10  Prayer  Two labs this week (telescope, interferometer)  The missing exams…  Project progress reports: I’m about 75% of the way done  Review: phaseshift   2 (PL  ) Approx.1: PL  d sin    E  stuff  1  ei E  stuff   e   e   i 2 i 2 E  stuff  cos( 2) I  I0 cos2 ( 2) Approx.2: sin   y L Fourier Transforms?  From last time: what did our two-slit analysis have to do with Fourier transforms? E  stuff  1  e  i   E~e ieach slit  E~  e i dY (this is the y-coordinate on the slits, not the y-coordinate on the screen) open areas  L2  2 nx    2i E~ aperture function  e dY an  f ( x) cos   dx L L 2  L   Adding up phases 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 slits  or , we need to add up a different set of phases… Etot  perhaps E0e  irel.to ref. islit1 likee0, 21, islit 2  e42, 63, ... etc. e ifinal slit screen  PL  y 2   2   for each slit two-slit PL  d sin   d I E    L  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.) Adding up phases, cont. … slits Etot  E0e irel.to ref. e islit1 e islit 2  ...  e ifinal slit  screen  PL  y 2   2   for each slit two-slit PL  d sin   d I E    L  Quick writing: graphically add these three vectors: 10 + 120 + 140  What about 10 + 190 + 1180 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 Thought question  How many “sub” peaks are there between the “main” peaks in a 5-slit interference pattern? a. 1 b. 2 c. 3 d. 4 e. 5 Five Slit Problem: Scanning Theta Note: for some reason he picked the overall reference phase to be about 20-30 Reading Quiz  How does the phase shift of a light wave switching between fast and slow media compare to the phase shift of a wave on a string switching between fast and slow media? a. The phase shift is the same b. The phase shift is the same for fast-to-slow, but reversed for slow-to-fast c. The phase shift is the same for slow-to-fast, but reversed for fast-to-slow d. The phase shift is reversed for both cases  What is the phase shift?  180 Remember these?  “Fresnel Equations” Just the same as strings If near perpendicular (1-D problem) v2  v1 n1  n2 2v2 2n1 r  t  v1  v2 n1  n2 v1  v2 n1  n2 2 2 R r T  1 r For arbitrary angle The Truth: if at an angle, you don’t n1 cos1  n2 cos2 2n1 cos1 always get a phase shift, even if rs polar .  ts polar .  going fast to slow. (Brewster) n1 cos1  n2 cos2 n1 cos1  n2 cos2 n1 cos2  n2 cos1 2n1 cos1 More Truth: sometimes phase rp polar.  t p polar . not just 180: complex n, shifts n1 cos2  n2 cos1 1 cos 2  ncomplex 2 cos1 ,netc. Back to 1D case  From low to high index: 180 phase shift  From high to low index: no phase shift  Quick writing: What does the thickness of this slab need to be to get constructive interference between the two rays? What changes if rays Rays drawn at an angle to make viewing easier. They’re really really are at an angle? perpendicular to surface. air thin glass thickness t air 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)  New situation  What does the thickness of the COATING need to be to get constructive interference between the two rays? Rays drawn at an angle to make viewing easier. They’re really perpendicular to surface. air thin coating, thickness t n = 1.3 thick glass, n = 1.5 Pretty pictures  What’s going on here? http://superphysics.netfirms. http://twilit.wordpress.com/2008/ com/pp_optics.html 03/15/bubbles-and-interference/ Demo/Video  Video: glass plates in sodium light  Demo: Soap film Interferometer  From lab 9: changing optical path length, yields ngas Interference! How does this disprove the ether?
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