Question

A ray of light is incident on a right angled isosceles prism parallel to its base as shown in the figure. Refractive index of the material of the prism is $\sqrt{2}$ . Then which of the following statement (s) is/are true?

• A. The reflection at P is total internal
• B. The reflection at Q is total internal
• C. The ray emerging at R is parallel to the ray incident at S
• D. Total deviation of the ray is $150^{\circ }$

Answer 1

Answer: (A), (C)

Critical angle ${\theta }_C={\sin }^{-1}\left(\frac{1}{\sqrt{2}}\right)=45^{\circ }$
Snell's law at points, $\left(\because n_1\sin {\theta }_1=n_2\sin {\theta }_2\right)$
$1\sin 45^{\circ }=\sqrt{2}\sin \theta$
$\therefore \theta =30^{\circ }$
At $P\because$ incidence angle at $P=75^{\circ }>{\theta }_C$.
$\therefore$ TIR at point $P$.
At $Q\because$ incidence angle at $Q=15^{\circ }<{\theta }_C$.
$\therefore$ Partial reflection and refraction at $Q$.
As $SP||QR$, emergent ray at $R$ is parallel to incident ray at $S$.
$\therefore$ Net deviation $=180^{\circ }$