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Problems 565 31. A fish below the surface of water with index of refraction n = 1.33 sees a star that he measures to be at 30* from the normal. What is the star's actual angle from the normal? 32. A straight light pipe with refractive index n, has a dielectric coating with index n 2 added for protection. The light pipe is usually within free space so that ns is typically unity. X3 U2·- 02: qs~iii (a) Light within the pipe is incident upon the first interface at angle 81. What are the angles O2 and Os? (b) What value of 01 will make Os just equal the critical angle for total internal reflection at the second interface? (c) How does this value differ from the critical angle if the coating was not present so that ni was directly in contact with n3? (d) If we require that total reflection occur at the first interface, what is the allowed range of incident angle 01. Must the coating have a larger or smaller index of refraction than the light pipe? 33. A spherical piece of glass of radius R has refractive index n. (a) A vertical light ray is incident at the distance x (x

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