Optics Ques 200
- A ray $O P$ of monochromatic light is incident on the face $A B$ of prism $A B C D$ 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 $C D$
(b) The ray comes out through face $A D$
(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 $120^{\circ}$
Show Answer
Answer:
Correct Answer: 200.(a, b, c)
Solution:
Formula:
- $\sqrt{3}=\frac{\sin 60^{\circ}}{\sin r}$
$ \begin{aligned} \therefore \quad r & =30^{\circ} \\ \theta _C & =\sin ^{-1} (\frac{1}{\sqrt{3}}) \text { or } \sin \theta _C=\frac{1}{\sqrt{3}} \\ & =0.577 \end{aligned} $
At point $Q$, angle of incidence inside the prism is $i=45^{\circ}$.
Since $\sin i=\frac{1}{\sqrt{2}}$ is greater than $\sin \theta _C=\frac{1}{\sqrt{2}}$, ray gets totally internally reflected at face $C D$. Path of ray of light after point $Q$ is shown in figure.
From the figure, we can see that angle between incident ray $O P$ and emergent ray $R S$ is $90^{\circ}$.
BETA
