Q. The refracting angle of a prism is $A$and the refractive index of the material of the prism is $\cot{(A/2)}.$The angle of minimum deviation of the prism is
A) $\pi + 2A$
B) $\pi - 2A$
C) $\frac{\pi}{2} + A$
D) $\frac{\pi}{2} - A$
Explanation
(b) $\mu = \cot{\frac{A}{2} = \frac{\sin{(\frac{A + \delta m}{2})}}{\sin{A/2}}}$
$or\frac{\cos\frac{A}{2}}{\sin\frac{A}{2}} = \frac{\sin{(\frac{A + \delta m}{2})}}{\sin{A/2}}$
$or\ \sin\left( 90{^\circ} - \frac{A}{2} \right) = \sin\left( \frac{A + \delta m}{2} \right)$
$or\ \ 90{^\circ} - \frac{A}{2} = \ \left( \frac{A + \delta m}{2} \right)$
$or\ \ 180{^\circ} - A = A + \ \delta m$
$\delta m = 180{^\circ} - 2A = \pi - 2A$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.