Answer
a. $38.1^{\circ}$.
b. $55.4^{\circ}$.
Work Step by Step
Total internal reflection occurs when the angle of incidence is greater than or equal to the critical angle.
At the critical angle, Snell’s law gives $n_{glass}sin\theta_{crit}= n_{air}sin90^{\circ}$.
a. $n_{glass}sin\theta_{crit}= n_{air}sin90^{\circ}$
$$1.62sin\theta_{crit}= 1.00 (1)$$
$$\theta_{crit}= 38.1^{\circ}$$
b. Use the same procedure as in part A.
$$n_{glass}sin\theta_{crit}= n_{water}sin90^{\circ}$$
$$1.62sin\theta_{crit}= 1.333 (1)$$
$$\theta_{crit}= 55.4^{\circ}$$
