Answer
The ray's angle with respect to the face of the crystal is $~~74^{\circ}$
Work Step by Step
We can use Snell's Law to find the ray's angle in the cubic zirconia crystal with respect to the normal:
$n_2~sin~\theta_2 = n_1~sin~\theta_1$
$sin~\theta_2 = \frac{n_1~sin~\theta_1}{n_2}$
$sin~\theta_2 = \frac{(1.46)~(sin~25^{\circ})}{2.18}$
$sin~\theta_2 = 0.283$
$\theta_2 = sin^{-1}~(0.283)$
$\theta_2 = 16^{\circ}$
We can find the ray's angle with respect to the face of the crystal:
$90^{\circ}-16^{\circ} = 74^{\circ}$
The ray's angle with respect to the face of the crystal is $~~74^{\circ}$
