Question

A stone placed at the bottom of a water tank appears raised by $80cm$. If the refractive index of water is $4/3$, find the actual depth of water in the tank.

Answer 1

Step 1: Given data,

Refractive index of water$=R.I=4/3$

Step 2: Finding the actual depth of water in the tank.

Let the actual depth of stone be $xcm$

Then observed depth$=(x-80)cm$

$$\begin{gathered} \text{R.I.}=\frac{\text{Actual depth}}{\text{observed depth}} \\ \frac{4}{3}=\frac{x}{x-80} \\ 4(x-80)=3x \\ 4x-3x=320 \\ x=320 \end{gathered}$$

Hence the actual depth of water in the tank is $320cm.$