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Announcements 11/14/11

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

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Announcements 11/14/11

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

  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 DPLs compare? • Each f is a multiple of f2! (Could have an overall reference phase for f1…not too important.) 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 q, we need to add up a different set of phases… perhaps like 0, 21, 42, 63, etc. slits screen

  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? • 1 • 2 • 3 • 4 • 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? • 0 • 45 • 90 • 180 • depends on whether it is s- or p-polarization

  9. Remember these? • “Fresnel Equations” If near perpendicular (1-D problem) 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) For arbitrary angle More Truth: sometimes phase shifts not just 180: can have complex n, complex q, etc. You can’t handle this much truth! 

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

  11. Rays drawn at an angle to make viewing easier. They’re really perpendicular to surface. Back to “near normal incidence” • 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? If rays at an angle… determine if above/ below Brewster angle (if p-polarization). air thin glass thickness t air

  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) = ml • Destructive interference: OPL ( any phase shifts) = (m+1/2) l

  13. 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, n = 1.3 thickness t thick glass, n = 1.5

  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: changing optical path length, yields ngas Interference! How does this disprove the ether?

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