Question

A ray of light passes through an equilateral glass prism in such a manner that the angle of incidence is equal to the angle of emergence and each of these angles is equal to $3/4$ of the angle of the prism. The angle of deviation is

• A. ${45}^{\circ }$
• B. ${39}^{\circ }$
• C. ${20}^{\circ }$
• D. ${30}^{\circ }$

Answer 1

The correct option is D ${30}^{\circ }$

In an equilateral triangle,
Angle or prism is
$\Rightarrow A={60}^{\circ }$
Given: $i=e=\frac{3}{4}A$
$\therefore i=\frac{3}{4}\times {60}^{\circ }={45}^{\circ }$
The minimum deviation produced by prism is,
${\delta }_m=i+e-A$
$\Rightarrow {\delta }_m=2i-A$
$\Rightarrow {\delta }_m=2\times {45}^{\circ }-A$
$\therefore {\delta }_m={90}^{\circ }-{60}^{\circ }={30}^{\circ }$

Why this question? Tip: It has been mentioned in question that $i$ and $e$ are equal, thus it is the case of minimum angle of deviation.