What is the refractive index of the material of a prism if the angle of minimum deviation for the prism of angle \( \displaystyle\frac{\pi}{3} \) is \( \displaystyle\frac{\pi}{6} \)?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \sqrt{2} \)
For a prism of angle A the refractive index is given by the prism formula in terms of the angle of minimum deviation \( \delta_m \).
\( A = \frac{\pi}{3} = 60^{\circ},\quad \delta_m = \frac{\pi}{6} = 30^{\circ} \)
\( \displaystyle \mu = \frac{\sin\left(\frac{A+\delta_m}{2}\right)}{\sin\left(\frac{A}{2}\right)} = \frac{\sin45^{\circ}}{\sin30^{\circ}} \)
\( \displaystyle \mu = \frac{1/\sqrt{2}}{1/2} = \sqrt{2} \)
Note: NTA picked this question from an NCERT (2026-27) exercise and changed the figures. Do not ignore NCERT while practising numericals.
NCERT (2026-27):
Exercises – …
