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1059_Physics ProblemsTechnical Physics

1059_Physics ProblemsTechnical Physics - 400 P37.56...

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400 Interference of Light Waves P37.56 At entrance, 1 00 30 0 1 38 2 . sin . . sin °= θ θ 2 21 2 = ° . Call t the unknown thickness. Then cos . 21 2 °= t a a t = ° cos . 21 2 tan . 21 2 °= c t c t = ° tan . 21 2 sin θ 1 2 = b c b t = ° ° 2 21 2 30 0 tan . sin . The net shift for the second ray, including the phase reversal on reflection of the first, is FIG. P37.56 2 2 an b λ where the factor n accounts for the shorter wavelength in the film. For constructive interference, we require 2 2 an b m = λ λ . The minimum thickness will be given by 2 2 0 an b = λ . λ 2 2 2 21 2 2 21 2 30 0 = = ° ° ° an b nt t cos . tan . sin . a f 590 2 1 38 21 2 2 21 2 30 0 2 57 nm 2 = × ° ° ° F H G I K J = . cos . tan . sin . . t t t = 115 nm P37.57 The shift between the two reflected waves is δ λ = 2 2 na b where a and b are as shown in the ray diagram, n is the index of refraction, and the term λ 2 is due to phase reversal at the top
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