A light ray from air is incident on a glass slab (\( \mu = 1.5 \)) as shown in the figure. It undergoes a total internal reflection and travels along AB. The thickness AC of the glass slab is 20 cm. The time taken by light to cross the glass slab after reflection is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 2 ns
After total internal reflection at A the ray travels along AB in glass with speed \( v = c/\mu \). The time is the path length AB divided by this speed.
The angle of incidence at A is \( 60^\circ \), and by the law of reflection the reflected ray AB also makes \( 60^\circ \) with the normal AC. In the right-angled triangle ACB with AC = 20 cm:
\( \displaystyle AB = \frac{AC}{\cos 60^\circ} = \frac{20}{0.5} = 40\,\mathrm{cm} = 0.4\,\mathrm{m} \)
\( \displaystyle v = \frac{c}{\mu} = \frac{3\times10^{8}}{1.5} = 2\times10^{8}\,\mathrm{m\,s^{-1}} \)
\( \displaystyle t = \frac{AB}{v} = \frac{0.4}{2\times10^{8}} = 2\times10^{-9}\,\mathrm{s} = 2\,\mathrm{ns} \)