Question

How is the refractive index of water related to the real depth and the apparent depth of a column of water ?

Answer 1

Let us table a tank full of water having a depth of d and it appears to be at a depth i.e a is apparent depth.

${\mu }_w$ is refractive index of water so now from snells law

${\mu }_w\sin i=\sin r$

${\mu }_w=\frac{\sin r}{\sin i}$ and for small angle; $\sin \theta =\theta =\tan \theta$

hence, ${\mu }_w=\frac{\tan r}{\tan i}$

$\tan r=\frac{A}{a},\tan i=\frac{A}{d}$

hence ${\mu }_w=\frac{d}{a}=\frac{\text{real depth}}{\text{apparent depth}}$