Question

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

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

Answer 1

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

Given:
Refractive index of glass with respect to water, ${\mu }_{gw}=\frac{9}{8}$
Refractive index of glass with respect to air, ${\mu }_{ga}=\frac{3}{2}$
Refractive index of water with respect to air, ${\mu }_{wa}=?$


We know that,

${\mu }_{ga}\times {\mu }_{wg}\times {\mu }_{aw}=1$

$\Rightarrow {\mu }_{ga}\times \frac{1}{{\mu }_{gw}}\times {\mu }_{aw}=1$

$\Rightarrow \frac{3}{2}\times \frac{1}{9/8}\times {\mu }_{aw}=1$

$\Rightarrow {\mu }_{aw}=\frac{3}{4}$

$\Rightarrow {\mu }_{wa}=\frac{1}{{\mu }_{aw}}=\frac{4}{3}$

Hence, option $\left(c\right)$ is the correct answer.