The angle of incidence in minimum deviation position for an equilateral prism is \( 60^\circ \). The refractive index of the prism is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \sqrt{3} \)
At the minimum deviation position the ray passes symmetrically through the prism: the angles of incidence and emergence are equal, and the refraction angle at each face is half the prism angle.
\( A = 60^\circ, \quad i = 60^\circ \)
\( \displaystyle r = \frac{A}{2} = 30^\circ \)
By Snell’s law at the first face:
\( \displaystyle \mu = \frac{\sin i}{\sin r} = \frac{\sin 60^\circ}{\sin 30^\circ} \)
\( \displaystyle \mu = \frac{\sqrt{3}/2}{1/2} = \sqrt{3} \)
The same result follows from \( \delta_m = 2i - A = 60^\circ \) and \( \mu = \sin\frac{A+\delta_m}{2}\Big/\sin\frac{A}{2} \).
Note: The same question was also asked in CUET (UG) 2023 on 30-05-2023 (Slot 2).