Question

The refractive index of air w.r.t glass is 2/3. The refractive index of the diamond w.r.t air is 12/5.What is the refractive index of glass w.r.t the diamond?

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{Refractive}\mathrm{index}\mathrm{of}\mathrm{air}\mathrm{w}.\mathrm{r}.\mathrm{t}\mathrm{glass},{\mathrm{\mu }}_1=\frac{2}{3} \\ \mathrm{Refractive}\mathrm{index}\mathrm{of}\mathrm{diamond}\mathrm{w}.\mathrm{r}.\mathrm{t}\mathrm{air}=\frac{12}{5} \\ \mathrm{or},\mathrm{Refractive}\mathrm{index}\mathrm{of}\mathrm{air}\mathrm{w}.\mathrm{r}.\mathrm{t}\mathrm{diamond},{\mathrm{\mu }}_2=\frac{5}{12} \\ \mathrm{Refractive}\mathrm{index}\mathrm{of}\mathrm{grass}\mathrm{w}.\mathrm{r}.\mathrm{t}\mathrm{diamond},\mathrm{\mu }=\frac{\mathrm{Refractive}\mathrm{index}\mathrm{of}\mathrm{air}\mathrm{w}.\mathrm{r}.\mathrm{t}\mathrm{diamond}}{\mathrm{Refractive}\mathrm{index}\mathrm{of}\mathrm{air}\mathrm{w}.\mathrm{r}.\mathrm{t}\mathrm{glass}} \\ \mathrm{\mu }=\frac{{\mathrm{\mu }}_2}{{\mathrm{\mu }}_1} \\ \mathrm{\mu }=\frac{{\displaystyle \raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$12$}\right.}}{{\displaystyle \raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}} \\ \mathrm{\mu }=\frac{5}{8} \end{gathered}$$