To a bird in air, a fish in water appears to be at \(30 \mathrm{~cm}\) from the surface. If refractive index of water with respect to air is \(\frac{4}{3}\), the real distance of bird from the surface is

The correct option is (C).

Consider the labeled figure. The fish appears at an apparent depth h๘ while the real depth is \(h\).
In triangle \(\mathrm{OPF}: \tan (\mathrm{i})=\frac{\mathrm{P}}{\mathrm{h}} \simeq \sin (\mathrm{i})\)
In triangle OPA: \(\tan (\mathrm{r})=\frac{\mathrm{P}}{\mathrm{h}^{\prime}} \simeq \sin (\mathrm{r})\)
For small angles \(\theta, \operatorname{tam} \theta \simeq \sin \theta\) can be taken.
Using smell's law of refraction: \(1 \times \sin (\mathrm{r})=\mu \times \sin (\mathrm{i})\)
Inserting expressions for \(\sin (\mathrm{i})\) and \(\sin (\mathrm{r}) 1 \times \frac{\mathrm{P}}{\mathrm{h}^{\prime}}=\mu \times \frac{\mathrm{P}}{\mathrm{h}}\)
\(\mathrm{h}=\mu \mathrm{h}^{\prime}\)
Given, \(\mathrm{h}^{\prime}=30 \mathrm{~cm}\) and \(\mu=\frac{4}{3}\), therefore real depth \(\mathrm{h}=40 \mathrm{~cm}\).