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1063_Physics ProblemsTechnical Physics

1063_Physics ProblemsTechnical Physics - 404 P37.65...

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404 Interference of Light Waves P37.65 For bright rings the gap t between surfaces is given by 2 1 2 t m = + F H G I K J λ . The first bright ring has m = 0 and the hundredth has m = 99. So, t = × = 1 2 99 5 500 10 24 9 9 . . a f e j m m µ . Call r b the ring radius. From the geometry of the figure at the right, t r r r R R r b b = F H I K 2 2 2 2 Since r r b << , we can expand in series: t r r r r R R r R r r r R r t r R b b b b b = F H G I K J + F H G I K J = = L N M O Q P = × L N M M O Q P P = 1 1 2 1 1 2 1 2 1 2 2 1 1 2 24 9 10 1 4 00 1 12 0 1 73 2 2 2 2 2 2 1 2 6 1 2 . . . . m m m cm e j FIG. P37.65 P37.66 E E E E i j R = + + = + + L N M O Q P + + + L N M O Q P 1 2 3 6 3 00 7 2 6 00 4 3 6 3 00 7 2 6 00 4 3 cos . cos . cos ± sin . sin . sin ± π π π π π π E i j R = − 2 13 7 70 . ± . ± E R = + − 2 13 7 70 2 2 . . a f a f at tan . . . F H G I K J = 1 7 70 2 13 7 99 at 4.44 rad Thus, E t P = + 7 99 4 44 . sin . ω rad b g . x y E 1 E 2 E 3 E R FIG. P37.66 P37.67 (a)
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