In Fig. 33-60, light enters a $90^{\circ}$ triangular prism at point $P$ with incident angle $\theta$, and then some of it refracts at point $Q$ with an angle of re. fraction of $90^{\circ} .$ (a) What is the index of refraction of the prism in terms of $\theta$ ? (b) What, numerically, is the maximum value that the index of refraction can have? Does light emerge at $Q$ if the incident angle at $P$ is (c) increased slightly and (d) decreased slightly?