The refractive index of water is \( \left(\displaystyle\frac{4}{3}\right) \) and that of glass is \( \left(\displaystyle\frac{3}{2}\right) \). If the speed of light in glass is \( 2 \times 10^{8}\,\mathrm{m/s} \), the speed of light in water will be
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( \left(\displaystyle\frac{9}{4}\right) \times 10^{8}\,\mathrm{m/s} \)
The refractive index of a medium is \( n = c/v \), so the speed of light in a medium is inversely proportional to its refractive index and \( n\,v \) is the same for every medium.
\( \displaystyle n_{w}\,v_{w} = n_{g}\,v_{g} \)
\( \displaystyle v_{w} = \frac{n_{g}}{n_{w}}\,v_{g} = \frac{3/2}{4/3} \times 2\times10^{8}\,\mathrm{m\,s^{-1}} \)
\( \displaystyle v_{w} = \frac{9}{8} \times 2\times10^{8} = \frac{9}{4}\times10^{8}\,\mathrm{m\,s^{-1}} \)
Water is optically less dense than glass, so light is faster in water, as the result shows.