The refractive index of an equilateral prism is \( \sqrt{3} \). The angle of incidence for which angle of deviation is minimum is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 60°
At minimum deviation the ray passes symmetrically through the prism, so the angle of refraction at the first face is half the angle of the prism, \( r = A/2 \). Snell's law at that face then gives the angle of incidence, \( \mu = \sin i/\sin r \).
For an equilateral prism \( A = 60^\circ \), so \( r = 30^\circ \).
\( \sin i = \mu\sin r = \sqrt{3}\sin30^\circ = \sqrt{3}\times\frac{1}{2} \)
\( \displaystyle \sin i = \frac{\sqrt{3}}{2} \Rightarrow i = 60^\circ \)
Check: the minimum deviation is \( \delta_{\min} = 2i - A = 120^\circ - 60^\circ = 60^\circ \).