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985_Physics ProblemsTechnical Physics

985_Physics ProblemsTechnical Physics - 326 The Nature of...

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326 The Nature of Light and the Laws of Geometric Optics P35.26 Refraction proceeds according to 1 00 1 66 1 2 . sin . sin a f a f θ θ = . (1) (a) For the normal component of velocity to be constant, v v 1 1 2 2 cos cos θ θ = or c c a f cos . cos θ θ 1 2 1 66 = F H G I K J . (2) We multiply Equations (1) and (2), obtaining: sin cos sin cos θ θ θ θ 1 1 2 2 = or sin sin 2 2 1 2 θ θ = . The solution θ θ 1 2 0 = = does not satisfy Equation (2) and must be rejected. The physical solution is 2 180 2 1 2 θ θ = °− or θ θ 2 1 90 0 = °− . . Then Equation (1) becomes: sin . cos θ θ 1 1 1 66 = , or tan . θ 1 1 66 = which yields θ 1 58 9 = ° . . (b) Light entering the glass slows down and makes a smaller angle with the normal. Both effects reduce the velocity component parallel to the surface of the glass, so that component cannot remain constant, or will remain constant only in the trivial case
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