Answer
The index of refraction of material 1 is $~~1.44$
Work Step by Step
We can write Snell's law:
$n_w~sin~\theta_1 = n_m~sin~\theta_2$
In this equation:
$n_w$ is the index of refraction of water
$n_m$ is the index of refraction of the material
We can use the data pair $(\theta_1, \theta_2) = (90^{\circ}, 67.5^{\circ})$
We can use Snell's law to find the index of refraction of the material:
$n_w~sin~\theta_1 = n_m~sin~\theta_2$
$n_m = \frac{n_w~sin~\theta_1}{sin~\theta_2}$
$n_m = \frac{1.33~sin~90^{\circ}}{sin~67.5^{\circ}}$
$n_m = 1.44$
The index of refraction of material 1 is $~~1.44$.
