A. H. Pfund€™s method for measuring the index of refraction of glass is illustrated in Figure P35.69. One face of a slab of thickness t is painted white, and a small hole scraped clear at point P serves as a source of diverging rays when the slab is illuminated from below. Ray PBB+ strikes the clear surface at the critical angle and is totally reflected, as are rays such as PCC+. Rays such as PAA+ emerge from the clear surface. On the painted surface there appears a dark circle of diameter d, surrounded by an illuminated region, or halo.
(a) Derive an equation for n in terms of the measured quantities d and t.
(b) What is the diameter of the dark circle if n = 1.52 for a slab 0.600 cm thick?
(c) If white light is used, the critical angle depends on color caused by dispersion. Is the inner edge of the white halo tinged with red light or violet light? Explain.

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Clear surface C B C B Painted surface