Question

A prism has a refracting angle $60^{\circ}$. A ray of given monochromatic light suffers minimum deviation of $38^{\circ}$ in passing through prism refractive index of the material of prism is :

• A. 1.5094
• B. 1.3056
• C. 0.7849
• D. 2.425

Answer 1

Answer: (A)

Here : Refracting angle $A=60^{\circ}$ minimum deviation $\delta m=38^{\circ}.$
The refractive index is given by the formula
$\mu= \frac{\sin \frac{A+\delta m}{2}}{\sin \frac{A}{2}}=\frac{\sin \frac{60^{\circ}+38^{\circ}}{2}}{\sin \frac{60^{\circ}}{2}}$
$= \frac{\sin 49^{\circ}}{\sin 30^{\circ}}=\frac{0.7547}{0.5}=1.5094$