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
$\sqrt3$, 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)

$\sqrt3 =\frac{sin \, 60^\circ}{sin \, r}$
$\therefore 20\,mm r=30^\circ$
$ 20\,mm \theta_C=sin^{-1}\big(\frac{1}{\sqrt3}\big)$
or $ 20\,mm sin \, \theta-C=\frac{1}{\sqrt3}$
$25\,mm =0.577$
At point Q, angle of incidence inside the prism is $i = 45{\circ}$
Since $sin\, i=\frac{1}{\sqrt2}$ is greater than $sin\, \theta_C=\frac{1}{\sqrt2}$, 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)