For an equilateral prism, it is found that angle of minimum deviation is equal to angle of the prism. Find the refractive index of material of the prism.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( \sqrt{3} \)
The prism formula gives the refractive index in terms of the angle of the prism A and the angle of minimum deviation \( \delta_m \). For an equilateral prism \( A = 60^\circ \), and here \( \delta_m = A = 60^\circ \).
\( \displaystyle \mu = \frac{\sin\left(\frac{A+\delta_m}{2}\right)}{\sin\left(\frac{A}{2}\right)} = \frac{\sin60^\circ}{\sin30^\circ} = \frac{\sqrt{3}/2}{1/2} = \sqrt{3} \)
Shortcut: When \( \delta_m = A \), the numerator becomes \( \sin A \), so \( \mu = \sin A/\sin(A/2) = 2\cos(A/2) = 2\cos30^\circ = \sqrt{3} \).