Question

A person is swimming 0.91 m beneath the surface of the water in a swimming pool. A child standing on the diving board drops a ball into the pool directly above the swimmer. The swimmer sees the ball dropped from a height of 5.4 m above the water.

From what height was the ball actually dropped?

Answer 1

Use the below relation to find out the height from which the ball actually dropped. apparent depth \(=\mathrm{d}\left(\frac{\mathrm{n}_{\text {cbseve }}}{\mathrm{n}_{\text {doject }}}\right)\)

Here, \(d\) is the actual depth and \(n\) is the refractive index for different things involved such as observer and object.

Apparent depth is \(5.4 \mathrm{~m}\).

$$ \begin{aligned} \mathrm{d} &=\operatorname{apparent} \text { depth }\left(\frac{\mathrm{n}_{\text {object }}}{\mathrm{n}_{\text {observer }}}\right) \\ &=(5.4 \mathrm{~m})\left(\frac{1}{1.333}\right) \\ &=4.05 \mathrm{~m} \end{aligned} $$