Answer
The index of refraction of material 1 is $~~1.7$
Work Step by Step
On the graph, note that $\theta_2 = 30.0^{\circ}$ when $n_2 = 1.7$
According to Snell's law:
$n_1~sin~\theta_1 = n_2~sin~\theta_2$
We can find $n_1$:
$n_1~sin~\theta_1 = n_2~sin~\theta_2$
$n_1 = \frac{n_2~sin~\theta_2}{sin~\theta_1}$
$n_1 = \frac{1.7~sin~30.0^{\circ}}{sin~30^{\circ}}$
$n_1 = 1.7$
The index of refraction of material 1 is $~~1.7$
