Question

Solve the following examples.
a. If the speed of light in a medium is 1.5 × 10⁸ m/s, what is the absolute refractive index of the medium?
b. If the absolute refractive indices of glass and water are 3/2 and 4/3 respectively, what is the refractive index of glass with respect to water?

Answer 1

a.
$$\begin{gathered} \mathrm{Absolute}\mathrm{refractive}\mathrm{index}\mathrm{of}\mathrm{a}\mathrm{medium},\mu =\frac{\mathrm{Speed}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{air}}{\mathrm{Speed}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{the}\mathrm{medium}} \\ \Rightarrow \mu =\frac{3\times {10}^8}{1.5\times {10}^8}=2 \end{gathered}$$

b.
$$\begin{gathered} {}_{\mathrm{a}}\mu _{\mathrm{g}}=\frac{3}{2}\mathrm{and}{}_{\mathrm{a}}\mu _{\mathrm{w}}=\frac{4}{3} \\ {}_{\mathrm{w}}\mu _{\mathrm{g}}=? \end{gathered}$$
where,
$$\begin{gathered} {}_{\mathrm{w}}\mu _{\mathrm{g}}=\mathrm{Refractive}\mathrm{index}\mathrm{of}\mathrm{glass}\mathrm{w}.\mathrm{r}.\mathrm{t}.\mathrm{water} \\ {}_{\mathrm{a}}\mathrm{\mu }_{\mathrm{g}}=\mathrm{Absolute}\mathrm{refractive}\mathrm{index}\mathrm{of}\mathrm{glass} \\ {}_{\mathrm{a}}\mathrm{\mu }_{\mathrm{w}}=\mathrm{Absolute}\mathrm{refractive}\mathrm{index}\mathrm{of}\mathrm{water} \end{gathered}$$
Now,
$$\begin{gathered} {}_{\mathrm{a}}\mu _{\mathrm{g}}=\frac{3}{2}\mathrm{and}{}_{\mathrm{a}}\mu _{\mathrm{w}}=\frac{4}{3} \\ {}_{\mathrm{w}}\mu _{\mathrm{g}}=\frac{{}_{\mathrm{a}}\mu _{\mathrm{g}}}{{}_{\mathrm{a}}\mu _{\mathrm{w}}}=\frac{3}{2}\times \frac{3}{4}=\frac{9}{8} \end{gathered}$$