p34_049 - 49. Let be the angle of incidence and 2 be the...

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49. Let θ be the angle of incidence and θ 2 be the angle of refraction at the left face of the plate. Let n be the index of refraction of the glass. Then, the law of refraction yields sin θ = n sin θ 2 . The angle of incidence at the right face is also θ 2 .I f θ 3 is the angle of emergence there, then n sin θ 2 = sin θ 3 . Thus sin θ 3 = sin θ and θ 3 = θ . The emerging ray is parallel to the incident ray. We wish to derive an expression for x in terms of θ .I f D is the length of the ray in the glass, then D cos θ 2 = t and D = t/ cos θ 2 . The angle α in the diagram equals θ θ 2 and x = D sin α = D sin( θ θ 2 ). Thus x = t sin( θ θ 2 ) cos θ 2 . If all the angles θ , θ 2 , θ 3 ,and θ θ 2 are small and measured in radians, then sin θ θ , sin θ 2 θ 2 , sin( θ θ 2 ) θ θ 2 ,andcos θ 2 1. Thus x t ( θ θ
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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