Question

The refractive index of water with respect to vacuum is 4/3 and the refractive index of vacuum to glass is 2/3. If the speed of light is 2x10⁸m/sec. Find the speed of light in
i) vacuum
ii) water

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right) \\ \mathrm{Refractive}\mathrm{index}\mathrm{of}\mathrm{vacuum}\mathrm{wrt}\mathrm{glass}=\frac{\mathrm{Speed}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{glass}}{\mathrm{Speed}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{vacuum}} \\ \frac{2}{3}=\frac{2\times {10}^8}{\mathrm{Speed}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{vacuum}} \\ \mathrm{So},\mathrm{speed}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{vacuum}\mathrm{is}3\times {10}^8\mathrm{m}/\mathrm{s} \\ \left(\mathrm{ii}\right) \\ \mathrm{Refractive}\mathrm{index}\mathrm{of}\mathrm{water}\mathrm{wrt}\mathrm{vacuum}=\frac{\mathrm{Speed}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{vacuum}}{\mathrm{Speed}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{water}} \\ \frac{4}{3}=\frac{3\times {10}^8}{\mathrm{Speed}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{vacuum}} \\ \mathrm{So},\mathrm{speed}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{water}\mathrm{is}2.25\times {10}^8\mathrm{m}/\mathrm{s} \end{gathered}$$