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1053_Physics ProblemsTechnical Physics

1053_Physics ProblemsTechnical Physics - 394 P37.38...

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394 Interference of Light Waves P37.38 The condition for bright fringes is 2 2 t n m n + = λ λ m = 1 2 3 , , , . From the sketch, observe that t R R R r R r R = + F H G I K J = F H G I K J = 1 1 1 2 2 2 2 2 2 cos θ θ a f . The condition for a bright fringe becomes r R m n 2 1 2 = F H G I K J λ . Thus, for fixed m and λ , nr 2 = constant . R θ r t FIG. P37.38 Therefore, n r n r f i liquid air 2 2 = and n liquid cm cm = = 1 00 1 50 1 31 1 31 2 2 . . . . a f a f a f . P37.39 For destructive interference in the air, 2 t m = λ . For 30 dark fringes, including the one where the plates meet, t = = × 29 600 2 8 70 10 6 nm m a f . . Therefore, the radius of the wire is r t = = = 2 8 70 4 35 . . m 2 m µ µ . FIG. P37.39 P37.40 For total darkness, we want destructive interference for reflected light for both 400 nm and 600 nm. With phase reversal at just one reflecting surface, the condition for destructive interference is
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