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 $= 180^{\circ}$