Question

A water pond appears to be $2.5\mathrm{m}$ deep. If the refractive index of water is $\frac{4}{3}$. Determine the actual depth of the pond.

Answer 1

Step 1: Given data.

Refractive index is $\left(\frac{4}{3}\right)$

Apparent depth is $2.5\mathrm{m}$.

Step 2: Find the actual or real depth.

We know that,

$\mathrm{Refractive}\mathrm{index}=\frac{\mathrm{Real}\mathrm{Depth}}{\mathrm{Apparent}\mathrm{Depth}}$

Putting the value in the equation,

$\frac{4}{3}=\frac{\mathrm{real}\mathrm{depth}}{2.5\mathrm{m}}$

$\begin{array}{rcl}\mathrm{real}\mathrm{depth}& =& \frac{2.5\times 4}{3}\\ & =& 3.33\mathrm{m}\end{array}$

Thus, the actual depth of the pond is $3.33\mathrm{m}$.