53. The refractive index of the material of the prism is √ 3; then the angle of minimum deviation of the prism is ?

53. The refractive index of the material of the prism is √3; then the angle of minimum deviation of the prism is ?

\( (a) \ 30^\circ \)

\( (b) \ 45^\circ \)

\( (c) \ 60^\circ \)

\( (d) \ 75^\circ \)

Answer :  \( (c) \ 60^\circ \)

\( \frac{\sin \frac{\delta_{\min} + A}{2}}{\sin \frac{A}{2}} = \mu \)

Assume \( A = 60^\circ \)

\( \frac{\sin \frac{\delta_{\min} + 60^\circ}{2}}{\sin \frac{60^\circ}{2}} = \sqrt{3} \)

\( \frac{\delta_{\min} + 60^\circ}{2} = 60^\circ \)

\( \delta_{\min} = 60^\circ \)