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?

• Correct answer
  A

  The refiection at $P$ is total internal.
• B

  The reflection at $Q$ is total internal.
• Correct answer
  C

  The ray emerging at $R$ is parallel to the ray incident at $S .$
• D

  Total deviation of the ray is $150^{\circ}$

Solution

Critical angle $\theta_{C}=\sin ^{-1}\left(\frac{1}{\sqrt{2}}\right)=45^{\circ}$ Snell's law at points, $\left(\because n_{1} \sin \theta_{1}=n_{2} \sin \theta_{2}\right)$ $1 \sin 45^{\circ}=\sqrt{2} \sin \theta$ $\therefore \quad \theta=30^{\circ}$ 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 $S P \| Q R$, emergent ray at $R$ is parallel to incid, ray at $S$. $\therefore$ Net deviation $=180^{\circ}$

Hence, the correct answer is options: 'A', 'C'.