Question

A ray of light incident on one face of an equilateral prism at ${60}^{\circ }$ enters and leaves the prism symmetrically. Refractive index of the prism material is:

• A. $1.5$
• B. $1.62$
• C. $1.73$
• D. $1.8$

Answer 1

The correct option is C $1.73$

Given that the prism is Equilateral. Thus, Prism angle $A={60}^o$

As the light leaves symmetrical, the condition matches with the conditions of minimum deviation. Thus, Minimum deviation angle is $D_m={60}^o$

Refractive index is given by $\mu =\frac{\sin (\frac{A+D_m}{2})}{\sin (\frac{A}{2})}=\frac{\sin (\frac{60+60}{2})}{\sin (\frac{60}{2})}=\frac{\sin {60}^o}{\sin {30}^o}=\sqrt{3}\approx 1.73$