lecture 33 - more interference

lecture 33 - more interference - Announcements 3/23/11...

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Unformatted text preview: Announcements 3/23/11 Prayer Two labs this week (telescope, interferometer) Review: ( 29 1 i E stuff e φ = × + ( 29 2 2 i i E stuff e e φ φ- + = × + cos( 2) E stuff φ = × 2 cos ( 2) I I φ = phaseshift 2 ( ) PL φ π λ = ∆ Approx.1: sin PL d θ ∆ = Approx.2: sin y L θ = Fourier Transforms? From last time: what did our two-slit analysis have to do with Fourier transforms? ( 29 1 i E stuff e φ = × + ~ each slit i E e φ → ∑ ~ i open areas E e dY φ → ∫ ~ " " i E aperture function e dY φ ∞-∞ × ∫ (this is the y-coordinate on the slits, not the y-coordinate on the screen) 2 2 2 2 ( )cos L n L nx a f x dx L L π- = ÷ ∫ compare to: Adding up phases … ( 29 rel.to ref. slit1 slit 2 final slit ... i i i i tot E E e e e e φ φ φ φ = + + + For an equally-spaced pattern of slits, how do the ∆ PLs compare? Each φ is a multiple of φ 1 ! (Could have an overall reference phase…not too important.) slits screen 2 foreachslit PL φ π λ ∆ = ÷ 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., etc....
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lecture 33 - more interference - Announcements 3/23/11...

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