Question

A man standing in a swimming pool looks at a stone lying at the bottom. The depth of the swimming pool is h. At what distance from the surface of water is the image of the stone formed? Take $\mu$ as refractive index of water.

• A. h
• B. $\mu$ h
• C. $\frac{h}{\mu }$
• D. $\frac{\mu }{h}$

Answer 1

The correct option is C $\frac{h}{\mu }$

From the figure, Stone $S$ lies at the bottom of the swimming pool at a depth $h$. When it is viewed from air perpendicular to the surface of the water, then it's image $I$ is seen at the depth $h^{\prime }$.

From the ray diagram,

Applying Snell's law at the interface of two media,

${\mu }_{water}Sini={\mu }_{air}Sinr$

We know, ${\mu }_{air}=1$

$\Rightarrow {\mu }_{water}Sini=Sinr$ ...[ 1 ]

In $\Delta SAB$

$tani=\frac{AB}{AS}$

In $\Delta IAB$

$tanr=\frac{AB}{AI}$

As angle $i$ and angle $r$ are very small, because all the light rays are entering the eye,

$tanii\approx Sini=\frac{AB}{AS}$

$tanir\approx Sinr=\frac{AB}{AI}$

Substituting values of $Sini$ and $Sinr$ and ${\mu }_{water}$ in equation 1, we have

$\mu \frac{AB}{AS}=\frac{AB}{AI}$

$\Rightarrow AI=\frac{AS}{\mu }$

We know, $AS=h$

$\Rightarrow h^{\prime }=\frac{h}{\mu }$

Hence, the correct answer is OPTION C.