Question

A ray $OP$ of monochromatic light is incident on the face $AB$
of prism $ABCD$ near vertex $B$ at an incident angle of $60^{\circ }$ (see
figure). If the refractive index of the material of the prism is
$\sqrt{3}$, which of the following is (are) correct?

• A. The ray gets totally internally reflected at face CD
• B. The ray comes out through face AD
• C. The angle between the incident ray and the emergent ray is 90${}^{\circ }$
• D. The angle between the incident ray and the emergent ray is 120${}^{\circ }$

Answer 1

Answer: (A), (B), (C)

$\sqrt{3}=\frac{sin60^{\circ }}{sinr}$
$\therefore 20mmr=30^{\circ }$
$20mm{\theta }_C=si{n}^{-1}\left(\frac{1}{\sqrt{3}}\right)$
or $20mmsin\theta -C=\frac{1}{\sqrt{3}}$
$25mm=0.577$
At point Q, angle of incidence inside the prism is $i=45\circ$
Since $sini=\frac{1}{\sqrt{2}}$ is greater than $sin{\theta }_C=\frac{1}{\sqrt{2}}$, ray gets totally
internally reflected at face CD Path of ray of light after point Q is shown in figure
From the figure, we can see that angle between incident ray
OP and emergent ray RS is 90${}^{\circ }$
Therefore, correct options are (a), (b) and (c)