Question

The refractive index of glass with respect to water is $\frac{9}{8}$. Refractive index of glass with respect to air is $\frac{3}{2}$. The refractive index of water with respect to air will be:

• A. $\frac{10}{3}$
• B. $\frac{4}{3}$
• C. $\frac{3}{4}$
• D. $\frac{3}{5}$

Answer 1

The correct option is B $\frac{4}{3}$

Refractive index of glass w.r.t water,
${}_w{\mu }_g=\frac{9}{8}$
$\Rightarrow \frac{{\mu }_g}{{\mu }_w}=\frac{9}{8}$
also, ${}_a{\mu }_g=\frac{{\mu }_g}{{\mu }_a}=\frac{3}{2}$
Refractive index of water w.r.t air,
${}_a{\mu }_w=\frac{{\mu }_w}{{\mu }_a}$
$\Rightarrow {}_a{\mu }_w=\frac{{\mu }_g}{{\mu }_a}\times \frac{{\mu }_w}{{\mu }_g}$
$\Rightarrow {}_a{\mu }_w=\frac{3}{2}\times \frac{1}{\left(\frac{9}{8}\right)}$
$\therefore {}_a{\mu }_w=\frac{4}{3}$
Hence, option $\left(b\right)$ is the correct answer.

Why this question? To understand the application of principle of reversibility in association with refractive index.