Answer
The index of refraction of material 1 is $~~1.6$
Work Step by Step
On the graph, note that $\theta_3 = 40.0^{\circ}$ when $n_3 = 1.6$
According to Snell's law:
$n_1~sin~\theta_1 = n_2~sin~\theta_2 = n_3~sin~\theta_3$
We can find $n_1$:
$n_1~sin~\theta_1 = n_3~sin~\theta_3$
$n_1 = \frac{n_3~sin~\theta_3}{sin~\theta_1}$
$n_1 = \frac{1.6~sin~40.0^{\circ}}{sin~40^{\circ}}$
$n_1 = 1.6$
The index of refraction of material 1 is $~~1.6$
