Question

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

Answer 1

Let the actual depth of the water be (x) cm. Since the stone appears raised by 80 cm, its apparent depth is (x − 80) cm.

\[\text{Refractive index} = \frac{\text{real depth}}{\text{apparent depth}}\]

\[\frac{4}{3} = \frac{x}{x-80}\]

4(x − 80) = 3x

4x − 320 = 3x

x = 320 cm

Therefore, the actual depth of the water is 320 cm.