Question

The refractive index of air with respect to glass is 2/3 and the refractive index of water with respect to air is 4/3. if the speed of light in glass is 2 x 10⁸m/s, find the speed of light in
(a) air
(b) water

Answer 1

$$\begin{gathered} \mathrm{Given}, \\ \mathrm{Refractive}\mathrm{inde}x\mathrm{of}\mathrm{air}\mathrm{with}\mathrm{respect}\mathrm{to}\mathrm{glass},{\mu }_{ag}=\frac{2}{3} \\ \mathrm{Refractive}\mathrm{index}\mathrm{of}\mathrm{water}\mathrm{with}\mathrm{respect}\mathrm{to}\mathrm{air},{\mu }_{wa}=\frac{4}{3} \\ \mathrm{Speed}\mathrm{of}\mathrm{light},c=3\times {10}^8\mathrm{m}{\mathrm{s}}^{-1} \\ \left(\mathrm{a}\right) \\ {\mu }_{\mathrm{ag}}=\frac{\mathrm{Speed}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{glass}}{\mathrm{Speed}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{air}} \\ \Rightarrow S\mathrm{peed}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{air}=\frac{2\times {10}^8}{{\displaystyle \frac{2}{3}}} \\ \Rightarrow \mathrm{Speed}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{air}=3\times {10}^8\mathrm{m}{\mathrm{s}}^{-1} \\ \left(\mathrm{b}\right) \\ {\mu }_{\mathrm{wa}}=\frac{\mathrm{Speed}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{air}}{\mathrm{Speed}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{water}} \\ \Rightarrow \mathrm{speed}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{water}=\frac{3\times {10}^8}{{\displaystyle \frac{4}{3}}}=\frac{9}{4}\times {10}^8 \\ \Rightarrow \mathrm{speed}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{water}=2.25\times {10}^8\mathrm{m}{\mathrm{s}}^{-1} \end{gathered}$$