Question

The minimum deviation produced by a hollow prism filled with a certain liquid to be ${30}^0$. The light ray is also found to be refracted at angle ${30}^0$. The refractive index of the liquid is

• A. $\sqrt{\frac{3}{2}}$
• B. $\sqrt{3}$
• C. $\sqrt{2}$
• D. $\frac{3}{2}$

Answer 1

The correct option is C $\sqrt{2}$

For minimum angle of deviation for a prism
$A=2r,\therefore A={60}^o$
Now $\mu =\frac{\sin \frac{60+30}{2}}{\sin \frac{60}{2}}=\frac{\sin {45}^o}{\sin {30}^o}=\frac{1}{\sqrt{2}}\times \frac{2}{1}=\sqrt{2}$