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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 ieach 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 irel.to ref. islit1 likee0, 21, islit 2 e42, 63, ... etc. e ifinal 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 irel.to ref. e islit1 e islit 2 ... e ifinal 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: 10 + 120 + 140 What about 10 + 190 + 1180 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 cos1 n2 cos2 2n1 cos1 always get a phase shift, even if rs polar . ts polar . going fast to slow. (Brewster) n1 cos1 n2 cos2 n1 cos1 n2 cos2 n1 cos2 n2 cos1 2n1 cos1 More Truth: sometimes phase rp polar. t p polar . not just 180: complex n, shifts n1 cos2 n2 cos1 1 cos 2 ncomplex 2 cos1 ,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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