Question

The refractive indices of glass and water w.r.t air are $\frac{3}{2}$ and $\frac{4}{3}$ respectively. The refractive index of glass with respect to water will be

• A. $\frac{8}{9}$
• B. $\frac{9}{8}$
• C. $\frac{7}{6}$
• D. None of these

Answer 1

The correct option is B

$\frac{9}{8}$

Step 1: Given parameters

Refractive index of glass = $\frac{3}{2}$

Refractive index of water = $\frac{4}{3}$

Step 2: The refractive index of glass with respect to water

$\mathrm{Refractive}\mathrm{index}\mathrm{of}\mathrm{glass}\mathrm{with}\mathrm{respect}\mathrm{to}\mathrm{water}=\frac{\mathrm{Refractive}\mathrm{index}\mathrm{of}\mathrm{glass}}{\mathrm{Refractive}\mathrm{index}\mathrm{of}\mathrm{water}}$

On substituting the values, we get,

$$\begin{gathered} \mathrm{Refractive}\mathrm{index}\mathrm{of}\mathrm{glass}\mathrm{with}\mathrm{respect}\mathrm{to}\mathrm{water}=\frac{\left({\displaystyle \frac{3}{2}}\right)}{\left({\displaystyle \frac{4}{3}}\right)} \\ =\frac{9}{8} \end{gathered}$$

Hence, the refractive index of glass with respect to water is $\frac{9}{8}$.So, the correct option is (B).