Question

If the absolute refractive index of Glass is 1.5 and that of water is 4/3 find the refractive index of water with respect to glass

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{If}{\mathrm{v}}_1\mathrm{is}\mathrm{the}\mathrm{velocity}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{vacuum} \\ {\mathrm{v}}_2\mathrm{is}\mathrm{the}\mathrm{velocity}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{glass} \\ {\mathrm{v}}_3\mathrm{is}\mathrm{the}\mathrm{velocity}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{water} \\ \mathrm{refractive}\mathrm{index}\mathrm{of}\mathrm{glass}\mathrm{with}\mathrm{respect}\mathrm{to}\mathrm{vacuum},{\mathrm{n}}_{\mathrm{g}}=\frac{{\mathrm{v}}_1}{{\mathrm{v}}_2}=\frac{3}{2} \\ \mathrm{refractive}\mathrm{index}\mathrm{of}\mathrm{water}\mathrm{with}\mathrm{respect}\mathrm{to}\mathrm{vacuum},{\mathrm{n}}_{\mathrm{w}}=\frac{{\mathrm{v}}_1}{{\mathrm{v}}_3}=\frac{4}{3} \\ \mathrm{refractive}\mathrm{index}\mathrm{of}\mathrm{water}\mathrm{with}\mathrm{respect}\mathrm{to}\mathrm{glass},{}_{\mathrm{g}}\mathrm{n}_{\mathrm{w}}=\frac{{\mathrm{v}}_2}{{\mathrm{v}}_3} \\ {}_{\mathrm{g}}\mathrm{n}_{\mathrm{w}}=\frac{{\mathrm{v}}_2}{{\mathrm{v}}_1}\times \frac{{\mathrm{v}}_1}{{\mathrm{v}}_3} \\ {}_{\mathrm{g}}\mathrm{n}_{\mathrm{w}}=\frac{2}{3}\times \frac{4}{3}=\frac{8}{9} \end{gathered}$$