Question

A coin is placed at the bottom of a 3 cm deep pond. The refractive index of water is 1.5. At what depth does the coin appear to be, as seen from above the pond?

Answer 1

Step 1:Assumptions of the quantities

Let, the apparent depth of the coin be D

Step 2: Explanation of the given quantities

The real depth of the pond, $\mathrm{d}=3\mathrm{cm}$

The refractive index of water, $\mathrm{\mu }=1.5$

Step 3: Calculation for the apparent depth

By using the relation,

$$\begin{gathered} \mathrm{Refractive}\mathrm{index}=\frac{\mathrm{real}\mathrm{depth}}{\mathrm{apparent}\mathrm{depth}} \\ \mathrm{\mu }=\frac{\mathrm{d}}{\mathrm{D}} \\ 1.5=\frac{3\mathrm{cm}}{\mathrm{D}} \\ \mathrm{D}=\frac{3}{1.5} \\ \mathrm{D}=2\mathrm{cm} \end{gathered}$$

Thus, the apparent depth of the coin is 2 cm.