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1071_Physics ProblemsTechnical Physics

# 1071_Physics ProblemsTechnical Physics - 412*P38.7...

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412 Diffraction Patterns and Polarization *P38.7 The rectangular patch on the wall is wider than it is tall. The aperture will be taller than it is wide. For horizontal spreading we have tan . . . sin . . θ θ λ width width width width width m 2 m m 0.012 2 m = = = = = × = × y L a a 0 110 4 5 0 012 2 1 632 8 10 5 18 10 9 5 For vertical spreading, similarly tan . . . sin . . θ λ θ height height m 2 m m 0.000 667 m = = = = × = × 0 006 4 5 0 000 667 1 632 8 10 9 49 10 9 4 a h P38.8 Equation 38.1 states that sin θ λ = m a , where m = ± ± ± 1 2 3 , , , . The requirement for m = 1 is from an analysis of the extra path distance traveled by ray 1 compared to ray 3 in Figure 38.5. This extra distance must be equal to λ 2 for destructive interference. When the source rays approach the slit at an angle β , there is a distance added to the path difference (of ray 1 compared to ray 3) of
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