The base angles of the triangular glass prism are $\alpha$= 30^o and its refractive index n=$\sqrt{2}$. Parallel rays as shown in the figure, are normally incident on their base. What is the angle between two emergent rays?

We can easily find out the angle between two emergent rays by using these simple steps.

As,

The base angles of the triangle (a) = 30°

Refractive Index (n) = √2

Let the incidence angle be i, the refractive index be r1 and r2.

Incidence angle (i) = 90-30 = 60°

Here, according to the formula of Snell's law of refraction,

$\frac{\sin \left(i\right)}{\sin \left(r1\right)}=\sqrt{2}$

$\frac{\sin \left(60\right)}{\sin \left(r1\right)}=\sqrt{2}$

on solving we get, r1 = 15°

So, the deviation caused by one single ray = 30-15 = 15°

and

The deviation caused by two rays = 2×15 = 30°.

Hence, The angle between two emergent rays is 30°.