You have a triangular prism made of glass of refractive index 1.60, with angles of $30^{\circ}-90^{\circ}-60^{\circ}$. The short side is oriented vertically. A horizontal ray hits the middle of the slanted side of the prism. Draw the path of a ray as it passes into and through the prism. Determine all angles for its trip through the prism.

Precious stones are often cut in a brilliant cut to maximize the amount of light reflected by the stone. The angles of the cut depend on the refractive properties of the type of stone. The optimal angles for a diamond are shown in the cross section below. The cut has reflectional symmetry across the axis shown. Find the measures of the indicated angles in the figure.

(a) Calculate the critical angle for a diamond surrounded by air. (b) Calculate the critical angle for a diamond under water. (c) Explain why a diamond sparkles less under water then in air.

A beam of light passes from glass with refractive index $1.58$ into water with a refractive index $1.33$. The angle of the refracted ray in water is $58.0^{\circ}$. Draw a sketch of the situation showing the interface between the media, the normal line, the incident ray, the reflected ray, the refracted ray, and the angles of these rays relative to the normal line.

Suppose you illuminate two thin slits by monochromatic coherent light in air and find that they produce their first interference minima at $\pm 35.20^{\circ}$ on either side of the central bright spot. You then immerse these slits in a transparent liquid and illuminate them with the same light. Now you find that the first minima occur at $\pm 19.46^{\circ}$ instead. What is the index of refraction of this liquid?

You are 1.8 m tall. Where should you place the top of a mirror on the wall so you can see the top of your head? Where should you stand with respect to the wall?