Question

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

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

Answer 1

Answer: (A)

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