The speed of light in a medium whose critical angle is 60° will be

The correct answer is Option (1) → \( 2.6\times10^{8}\,\mathrm{m/s} \)

At the critical angle \( C \) the refracted ray grazes the boundary with air, so \( \sin C = 1/\mu \) for light going from the medium into air. The speed in the medium is \( v = c/\mu \).

    \( \displaystyle \mu = \frac{1}{\sin60^\circ} = \frac{2}{\sqrt{3}} \approx 1.155 \)

    \( \displaystyle v = \frac{c}{\mu} = \frac{3\times10^{8}}{1.155}\,\mathrm{m/s} \approx 2.6\times10^{8}\,\mathrm{m/s} \)

Shortcut: Because \( \mu = 1/\sin C \), the speed is simply \( v = c\sin C = 3\times10^{8}\times0.866\,\mathrm{m/s} \approx 2.6\times10^{8}\,\mathrm{m/s} \).