A ray of light passes through an equilateral glass prism such that the angle of incidence (i) = angle of emergence (e). If the angle of emergence is 0.75 times the angle of prism, the refractive index of the prism will be
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( \sqrt{2} \)
When \( i = e \), the ray passes through the prism symmetrically: this is the condition of minimum deviation, and the angles of refraction at the two faces are equal, \( r_1 = r_2 = A/2 \).
\( A = 60^\circ \ \text{(equilateral prism)} \)
\( i = e = 0.75 \times 60^\circ = 45^\circ \)
\( r = A/2 = 30^\circ \)
By Snell's law at the first face,
\( \displaystyle \mu = \frac{\sin i}{\sin r} = \frac{\sin 45^\circ}{\sin 30^\circ} = \frac{1/\sqrt{2}}{1/2} = \sqrt{2} \)