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HW-23Solutions-03-28-08

# HW-23Solutions-03-28-08 - Lehigh University HW-23 Solutions...

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Lehigh University Physics 21, Spring 2008 April 2, 2008 HW-23 Solutions 23-1. (HRW 33-67) In Fig. 33-65 , light enters a 90° triangular prism at point P with incident angle , and then some of it refracts at point Q with an angle of refraction of 90°. (a) What is the index of refraction of the prism in terms of ? (b) What, numerically, is the maximum value that the index of refraction can have? Does light emerge at Q if the incident angle at P is (c) increased slightly and (d) decreased slightly? Solution: 67. (a) A ray diagram is shown below. Let θ 1 be the angle of incidence and θ 2 be the angle of refraction at the first surface. Let θ 3 be the angle of incidence at the second surface. The angle of refraction there is θ 4 = 90°. The law of refraction, applied to the second surface, yields n sin θ 3 = sin θ 4 = 1. As shown in the diagram, the normals to the surfaces at P and Q are perpendicular to each other. The interior angles of the triangle formed by the ray and the two normals must sum to 180°, so θ 3 = 90° – θ 2 and sin sin cos sin . θ θ θ θ 3 2 2 2 2 90 1 = °− = = b g

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HW-23Solutions-03-28-08 - Lehigh University HW-23 Solutions...

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