Lect06 - Le cture6: Wave Re w, C s vie rystallography, and...

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Lecture 6, p. 1 Lecture 6: Waves Review, Crystallography, and Examples

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Lecture 6, p. 2 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?
Lecture 6, p. 3 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 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 0 0 0 -λ/ d 0 λ/ d φ θ φ θ -λ/ d 0 λ/ d 0 0 -λ/ d 0 λ/ d φ θ

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Lecture 6, p. 4
Lecture 6, p. 5 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. What is the slit spacing , d ? 2. If the wavelength, λ, is increased, what happens to the width of the principal maxima? L y d θ

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Lecture 6, p. 6 ACT 1: Multiple Slits 1. In 2-slit interference, the first minimum corresponds to φ = π . For 3-slits, we have a secondary maximum at φ = π (see diagram). What is the intensity of this secondary maximum? a) φ = π /2 b) φ =2 π /3 c) φ =3 π /4 2. What value of φ corresponds to the first zero of the 3-slit interference pattern? a) I 1 b) 1.5 I 1 c) 3 I 1 φ 0 -2π I 0 9I 1 φ = ? I =? 3. What value of φ corresponds to the first zero of the 4 -slit interference pattern? a) φ = π /2 b) φ =2 π /3 c) φ =3 π /4
Lecture 6, p. 7 Light of wavelength λ is incident on an N -slit system with slit width a and slit spacing d . 1. The intensity I as a function of y at a viewing screen located a distance L from the slits is shown to the right. L >> d, y, a

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This note was uploaded on 02/21/2011 for the course PHYS 214 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.

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Lect06 - Le cture6: Wave Re w, C s vie rystallography, and...

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