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# 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 =
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
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
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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Lect06 - Lecture 6 Waves Review Crystallography and...

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