Answer
The index of refraction of material 2 is impossible to calculate without more information.
Work Step by Step
On the graph, note that $\theta_3 = 40.0^{\circ}$ when $n_3 = 1.6$
According to Snell's law:
$n_1~sin~\theta_1 = n_2~sin~\theta_2 = n_3~sin~\theta_3$
Without knowing $\theta_2$, we can not calculate $n_2$, the index of refraction of material 2.
The index of refraction of material 2 is impossible to calculate without more information.
