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# lecture21 - Physics 102 Lecture 21 Diffraction Gratings...

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Diffraction, Gratings, Resolving Power Physics 102: Lecture 21

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Recall Interference (at least 2 coherent waves) Constructive (full wavelength difference) Destructive (half wavelength difference) Light (1 source, but different paths) last lecture Thin Films Double slit today Multiple slit x-ray diffraction from crystal Diffraction/single slit 5
But first: Thin Film Practice n glass = 1.5 n water = 1.3 n = 1.0 (air) t 1 2 δ 1 = ½ δ 2 = 0 + 2t / λ glass = 2t n glass / λ 0 = (2)(167)(1.5)/500) =1 Blue light ( λ ο = 500 nm ) incident on a glass ( n glass = 1.5 ) cover slip ( t = 167 nm ) floating on top of water ( n water = 1.3 ). Is the interference constructive or destructive or neither ? Phase shift = δ 2 δ 1 = ½ wavelength 45 Reflection at air-film interface only

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Young’s double slit/rays Bright spots Shadow This is not what is actually seen!
Young’s double slit/Huygens’ principle Every point on a wave front acts as a source of tiny wavelets that move forward.

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Young’s double slit/Huygens’ principle Every point on a wave front acts as a source of tiny wavelets that move forward.    dsin θ = m λ m = 0 m = +1 m = -1 m = -2 m = +2 θ
d Path length difference d Double Slit Review/ACT L = d sin θ 8 2)    dsin θ = (m + 1 2 ) λ 1)    dsin θ = m λ where m = 0, or 1, or 2, ... Which condition gives destructive interference? d sin( θ ) θ θ θ

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d Path length difference 1-2 Multiple Slits: (Diffraction Grating – N slits with spacing d) θ θ L = d sin θ 13    dsin θ = m λ Constructive interference for all paths when d Path length difference 1-3 = 2d sin θ d 3 Path length difference 1-4 = 3d sin θ = λ = 2 λ = 3 λ 4 1 2
N slits with spacing d Constructive Interference Maxima are at:    sin θ = m λ d * screen VERY far away θ Diffraction Grating Same as for Young’s Double Slit !

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d Preflight 21.1 L 15 d 1 2 3 All 3 rays are interfering constructively at the point shown. If
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