Answer
We can rank the materials according to the index of refraction:
$a \gt b \gt c$
Work Step by Step
Let $n_a$ be the index of refraction of material $a$
Let $\theta_a$ be the angle between the incident ray and a horizontal line.
Let $n_b$ be the index of refraction of material $b$
Let $\theta_b$ be the angle between the refracted ray and a horizontal line.
Note that $\theta_b \gt \theta_a$
Then $sin~\theta_b \gt sin~\theta_a$
According to Snell's law:
$n_a~sin~\theta_a = n_b~sin~\theta_b$
$\frac{n_a}{n_b} = \frac{sin~\theta_b}{sin~\theta_a} \gt 1$
Therefore, $n_a \gt n_b$
Let $n_b$ be the index of refraction of material $b$
Let $\theta_b$ be the angle between the incident ray and a vertical line.
Let $n_c$ be the index of refraction of material $c$
Let $\theta_c$ be the angle between the refracted ray and a vertical line.
Note that $\theta_c \gt \theta_b$
Then $sin~\theta_c \gt sin~\theta_b$
According to Snell's law:
$n_b~sin~\theta_b = n_c~sin~\theta_c$
$\frac{n_b}{n_c} = \frac{sin~\theta_c}{sin~\theta_b} \gt 1$
Therefore, $n_b \gt n_c$
We can rank the materials according to the index of refraction:
$a \gt b \gt c$
