Question

A person is lying on a diving board 3.00 m above the surface of the water in a swimming pool. She looks at a penny that is on the bottom of the pool directly below her. To her, the penny appears to be a distance of 8.00 m from her.

Required:
What is the depth of the water at this point?

Answer 1

Answer:

The  depth of water at the point is  $d_A = 6.55 \ m$

Explanation:

From the question we are told that

   The height of the person above water   is  $d = 3.00 \ m$

   The distance  of the coin as seen by the person  is $d' = 8.00 \ m$

Generally the apparent depth is mathematically represented as

      $d_a = \frac{d_A}{n}$

Here $d_A$ is the actual depth of water while  n is the refractive index of water with a constant value $n = 1.33$

Now from the point the person is the apparent depth is evaluated as

     $d_a = d'-d$

=>   $d_a = 8 - 3$

=>  $d_a = 5 \ m$

So

     $5 = \frac{d_A}{1.33}$

=>   $d_A = 5 * 1.33$

=>   $d_A = 6.55 \ m$