Question

A ray of light is incident at an angle of 60\[^\circ \] on one face of a prism of angle 30$^\circ $. The emergent ray of light makes an angle of 30$^\circ $ with incident ray. The angle made by the emergent ray with second face of prism will be:
A. 30$^\circ $
B. 90$^\circ $
C. 0$^\circ $
D. 45$^\circ $

Answer 1

Hint:We can try to implement the concept of deviation due to a prism to solve this question. One should keep in mind that if the angle of incidence is zero then it means the light Ray is travelling perpendicular to the medium hence there would be no refraction.

Formula used:
$\delta = {i_1} + {i_2} - A$
$\delta$ is the angle of deviation, ${i_1}$ and ${i_2}$ are the angle of incidence at first and second refracting surfaces respectively and A is the angle of the prism.

Complete step by step answer:
Given, the angle of incidence at the first refracting surface of the prism, ${i_1}$$ = 60^\circ $.
The angle of the prism A$ = 30^\circ $.
The deviation of the incident ray from the emergent ray i.e. the angle of deviation$\delta = 30^\circ $.
We know that$\delta = {i_1} + {i_2} - A$.
Using the above equation we can find the angle of incidence at the second refracting surface of the prism,
$
30 = 60 + {i_2} - 30 \\
\Rightarrow {i_2} = 0^\circ \\ $
Since the angle of incidence at the second refracting surface is zero therefore the angle of refraction should be equal to zero. So there is no refraction at the second surface of the prism.Therefore the emergent ray that is the second refracted Ray makes an angle of 90$^\circ $ with the second refracting surface.

Hence, option B is the correct answer.

Note: Students should take care while using the angle of incidence and angle of refraction as it is the angle made by the incident ray and emergent ray with the normal and not with the refracting surface of the prism.If the angle of incidence is zero then it means the light Ray is travelling perpendicular to the medium hence there would be no refraction i.e. the emergent ray will make 90 degree with the refracting surface of the prism.