A narrow beam of light is incident on a 30? ? 60? ? 90? prism as shown. The index of refraction of the prism is n=2.1. From which side of the prism does the beam emerge: (a) from AB, (b) from BC, (c) from AC, (d) from all sides?

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**A+ Work!! 100% CORRECT PHYSICS TUTORIAL

INCLUDES ANSWERS TO THE FOLLOWING QUESTIONS

Problem 1. A narrow beam of light is incident on a 30? ? 60? ? 90? prism as shown. The index of refraction of the prism is n=2.1. From which side of the prism does the beam emerge: (a) from AB, (b) from BC, (c) from AC, (d) from all sides? [1 point]

Problem 2. It was once suggested that the mirror for an astronomical telescope be produced by rotating a ?at disk of mercury at a prescribed angular velocity ? about a vertical axis. (a) What is the equation of the mirror surface z=h(r) so obtained? [2 points]

(b) How fast must the disk be rotated to obtain a F=10 cm focal length convex mirror? [1 point]

Problem 3. A beam of light has a small wavelength spread ?? about a central wavelength ?. The beam travels in vacuum until it enters a glass plate at an angle ?1 relative to the normal to the plate, as shown in the ?gure. The index of refraction of the glass is given by n(?). The angular spread ??2 of the refracted beam is given by (a) ??2 = | n ??|, (b) ??2 = | dn(?) ??|, (c) ??2 = | ? dn ??|, (d) ??2 = | sin ?2 ?? |, (e) ??2 = | tan ?2 dn(? ??|. [3 points]

Problem 4. Fermats principle of least time. Light ray propagates from P in a medium with refraction index n1 to Q in medium with n2 , see Figure. It strikes the interface at point x. (a) Calculate the time t(x) at which light arrives at Q as a function of x. [1 point]

(b) Optimize the value of t(x) with respect to x, and show using geometry, that the optimal trajectory satis?es Snells law, n1 sin ?1 = n2 sin ?2 . [2 points]

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