Midterm 3 Review

# Midterm 3 Review - Midterm 3 Review One formula sheet...

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Midterm 3 Review One formula sheet allowed

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Interference and Diffraction Superposition principle: The net electric field at any location is vector sum of the electric fields contributed by all sources. Diffraction is interference due to an aperture.
Two emitters: E 1 E 2 Fields in crossing point ( ) ( ) t E E t E E ω cos cos 0 2 0 1 = = Superposition: ( ) t E E E E cos 2 0 2 1 = + = Amplitude increases twice: constructive interference Interference: Constructive

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E 1 E 2 ( ) ( ) ( ) π ω + + = + = t t E E E E cos cos 0 2 1 ( ) ( ) + = = t E E t E E cos cos 0 2 0 1 ( ) t cos - 0 = Two waves are 180 0 out of phase: destructive interference Interference: Destructive
Maxima with twice the amplitude occur when phase shift between two waves is 0, 2 π , 4 , 6 (Or path difference is 0, λ , 2 λ …) Minima with zero amplitude occur when phase shift between two waves is , 3 , 5 (Or path difference is 0, λ /2, 3 λ /2…) Interference detector

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Two separated sources Point C on screen is very far from sources C normal Need to know phase difference Very far: angle ACB is very small Path AC and BC are equal Path difference: ) sin( θ d l = Δ If Δ l = 0, λ , 2 λ , 3 λ , 4 λ … - maximum If Δ l = λ /2, 3 λ /2, 5 λ /2 … - minimum
Diffraction: Interference due to an Aperture ) sin( θ λ d m = Or Fourier transform of Aperture function

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Spatial Coherence Each point on extended source is independent source of light If extended source is small and the slits are far away interference can still occur when, g ≫ ²
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