Chapter 43: Problem 41

Question: Two materials A and B have refractive indices of n₁=1.667 and n=1.586 resp.

1.

Find the critical angle for total internal reflection at an interface between the two materials

2.

In which direction must an incident ray be propagating if it is to be totally internally reflected?

Solution: Total internal reflection means that $\theta_2={\pi\over 2}$, hence

$$n_1\sin\theta_c~=~n_2$$

which leads to $\theta_1=72.1^o$, as measured from the normal. The ray must be propagating from A into B.