995_Physics ProblemsTechnical Physics

995_Physics ProblemsTechnical Physics - 336 The Nature of...

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336 The Nature of Light and the Laws of Geometric Optics (b) At entry, S S n n 2 1 2 2 1 1 1 42419 2419 1 0828 =− + F H G I K J = + = . . . af a f . At exit, S S 3 2 = . . Overall, S S S S S S 3 1 3 2 2 1 2 0685 = F H G I K J F H G I K J == .. or 68 5% . . P35.58 Define T n n = + 4 1 2 as the transmission coefficient for one encounter with an interface. For diamond and air, it is 0.828, as in Problem 57. As shown in the figure, the total amount transmitted is TT T T T T T n 22 2 2 4 2 6 2 2 111 1 +− ++ + a f …… We have 1 1 0 828 0 172 −=− = T so the total transmission is 0 828 1 0 172 0 172 0 172 4 6 . . a f a f a f a f ++++ . To sum this series, define F = 1 0 172 0 172 0 172 246 ... . Note that 0 172 0 172 0 172 0 172 4 6 . . afaf F =+++ , and 1 0172 1 4 6 += + + + + = . . FF . FIG. P35.58 Then, 1 0 172 2 . or F = 1 10 1 7 2 2 . . The overall transmission is then 1 7 2 0706 2 2 . . . = or 70 6% . . P35.59 Define n 1 to be the index of refraction of the surrounding medium and n 2 to be that for the prism material. We can use the critical angle of 42.0° to find the
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