A light ray enters through a right angled prism at point P with the angle of incidence $30^\circ$ as shown in figure. It travels through the prism parallel to its base $BC$ and emerges along the face $AC$. The refractive index of the prism is:
With right angle at apex A and ray parallel to BC inside, then grazing AC at critical angle: $\tan C = 1/2$, so $n = \sec C = \dfrac{\sqrt 5}{2}$.