Lect06 - Lecture 6: Waves Review, Crystallography, and...

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Lecture 6, p. 1 Lecture 6: Waves Review, Crystallography, and Examples
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Single Single - - Slit Slit Diffraction (from L4) Diffraction (from L4) Slit of width a. Where are the minima? Use Huygens’ principle: treat each point across the opening of the slit as a wave source. The first minimum is at an angle such that the light from the top and the middle of the slit destructively interfere . This works, because for every point in the top half, there is a corresponding point in the bottom half that cancels it. θ a/2 δ min sin 2 2 a λ δ θ = = min sin a = P Incident Wave (wavelength λ ) y L a The second minimum is at an angle such that the light from the top and a point at a/4 destructively interfere: min,2 sin 4 2 a = = min,2 2 sin a = Location of nth-minimum : min, sin n n a =
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Lecture 6, p. 3 Single-Slit Diffraction Example W = 1 cm L = 2 m a θ Suppose that when we pass red light ( λ = 600 nm ) through a slit of unknown width a , the width of the spot (the distance between the first zeros on each side of the bright peak) is W = 1 cm on a screen that is L = 2 m behind the slit. How wide is the slit?
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Lecture 6, p. 4
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Lecture 6, p. 5 Multiple Slit Interference (from L4) The positions of the principal maxima occur at φ = 0, ± 2 π , ± 4 π , . .. where φ is the phase between adjacent slits. θ = 0, ±λ /d , ± 2 λ /d, . .. The intensity at the peak of a principal maximum goes as N 2 . 3 slits: A tot = 3A 1 I tot = 9I 1 . N slits: I N = N 2 I 1 . Between two principal maxima there are N-1 zeros and N-2 secondary maxima The peak width 1/N . The total power in a principal maximum is proportional to N 2 (1/N) = N. 0 -2π I 4 0 16I 1 N=4 0 -2π I 5 0 25I 1 N=5 0 -2π I 3 0 9I 1 N=3 -λ/ d 0 λ/ d φ θ φ θ -λ/ d 0 λ/ d -λ/ d 0 λ/ d φ θ
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Lecture 4, p 6 Act 1 Light interfering from 10 equally spaced slits initially illuminates a screen. Now we double the number of slits, keeping the spacing constant. 1. What happens to the intensity I at the principal maxima? a. stays same (I) b. doubles (2I) c. quadruples (4I) 2. What happens to the net power on the screen? a. stays same b. doubles c. quadruples
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Lecture 6, p. 7 Multiple-slit Example Three narrow slits with equal spacing d are at a distance L = 1.4 m away from a screen. The slits are illuminated at normal incidence with light of wavelength λ = 570 nm . The first principal maximum on the screen is at y = 2.0 mm . 1.
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This note was uploaded on 01/19/2012 for the course PHYS 214 taught by Professor Staff during the Fall '08 term at University of Illinois, Urbana Champaign.

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Lect06 - Lecture 6: Waves Review, Crystallography, and...

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