The equation for n in terms of d and t .

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Chapter 35, Problem 76AP

(a)

To determine

The equation for n in terms of d and t.

(b)

To determine

The diameter of the dark circle.

(c)

To determine

The color of the light in the inner edge of the white halo.

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71. A light ray enters a rectangular block of plastic at an angle& 1 ! 45.0° and emerges at an angle & 2 ! 76.0°, as shownin Figure P35.71. (a) Determine the index of refraction ofthe plastic. (b) If the light ray enters the plastic at a pointL ! 50.0 cm from the bottom edge, how long does it takethe light ray to travel through the plastic?

A. H. Pfund’s method for measuring the index of refraction of glass is illustrated as shown. 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, dispersion causes the critical angle to depend on color. Is the inner edge of the white halo tinged with red light or with violet light? Explain.

A. H. Pfund's method for measuring the index of refraction of glass is illustrated in the figure below. 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. Clear surface C BA C' B' P Painted surface (a) Derive an equation for n in terms of the measured quantities d and t. n = (b) What is the diameter of the dark circle if n = 1.47 for a slab 0.560 cm thick? cm (c) If white light is used, dispersion caused the critical angle to depend on color. Is the inner edge of the white halo tinged with red light or with violet light? O red O violet