A ray of light passes through an equilateral prism in minimum deviation position. If the angle of emergence is \( \displaystyle\frac{3}{4} \) times of angle of prism, then the refractive index of material of prism is-
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1.414
In the minimum deviation position the ray passes symmetrically through the prism: the angle of emergence equals the angle of incidence, and each angle of refraction inside is half the angle of the prism.
\( A = 60^\circ\ \text{(equilateral prism)} \)
\( \displaystyle i = e = \frac{3}{4} \times 60^\circ = 45^\circ \)
\( \displaystyle r = \frac{A}{2} = 30^\circ \)
By Snell’s law at the first face:
\( \displaystyle \mu = \frac{\sin i}{\sin r} = \frac{\sin 45^\circ}{\sin 30^\circ} \)
\( \displaystyle \mu = \frac{1/\sqrt{2}}{1/2} = \sqrt{2} \approx 1.414 \)