Question

Colored light is an incident on a prism. If the refractive index for given color of light is $\sqrt{3}$ and the angle of the prism is $60°$, the angle of minimum deviation is _________.

• A. $60°$
• B. $30°$
• C. $45°$
• D. $15°$

Answer 1

The correct option is A

$60°$

Step 1: Given data and formula used

Given:

Prism angle $\angle A=60°$

Refractive index $\mu =\sqrt{3}$

Formula used:

$\mu =\frac{\sin \left({\displaystyle \frac{A+\delta }{2}}\right)}{\sin \left({\displaystyle \frac{A}{2}}\right)}$

Step 2: Calculation for the angle of deviation $\delta$

On putting given value in formula used

$$\begin{gathered} \sqrt{3}=\frac{\sin \left({\displaystyle \frac{60+\delta }{2}}\right)}{\sin \left({\displaystyle \frac{60}{2}}\right)}=\frac{\sin \left({\displaystyle \frac{60+\delta }{2}}\right)}{\sin \left({\displaystyle 30}\right)} \\ \sqrt{3}\times \frac{1}{2}=\sin \left(\frac{60+\delta }{2}\right) \\ \frac{60+\delta }{2}=60° \\ \delta =60° \end{gathered}$$

Hence, the correct option is (a).