Answer
The index of refraction of material 2 is $~~1.44$
Work Step by Step
We can write Snell's law:
$n_w~sin~\theta_2 = n_i~sin~\theta_1$
In this equation:
$n_w$ is the index of refraction of water
$n_i$ is the index of refraction of the material
We can use the data pair $(\theta_1, \theta_2) = (67.5^{\circ}, 90^{\circ})$
We can use Snell's law to find the index of refraction of the material:
$n_w~sin~\theta_2 = n_i~sin~\theta_1$
$n_i = \frac{n_w~sin~\theta_2}{sin~\theta_1}$
$n_i = \frac{1.33~sin~90^{\circ}}{sin~67.5^{\circ}}$
$n_i = 1.44$
The index of refraction of material 2 is $~~1.44$.
