A ray of light from air passes through an equilateral triangular glass prism and undergoes minimum deviation when the angle of incidence is \( \frac{3}{4} \) of the angle of the prism. The speed of light in prism is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 2.12 \times 10^{8}\,\mathrm{m/s} \)
At minimum deviation the ray passes symmetrically through the prism, so \( r_1 = r_2 = A/2 \) and the refractive index is \( \mu = \sin i / \sin (A/2) \). An equilateral prism has \( A = 60^\circ \).
\( \displaystyle i = \frac{3}{4} \times 60^\circ = 45^\circ \)
\( \displaystyle r = \frac{A}{2} = 30^\circ \)
\( \displaystyle \mu = \frac{\sin 45^\circ}{\sin 30^\circ} = \frac{1/\sqrt{2}}{1/2} = \sqrt{2} = 1.414 \)
\( \displaystyle v = \frac{c}{\mu} = \frac{3\times10^{8}}{1.414} = 2.12\times10^{8}\,\mathrm{m\,s^{-1}} \)