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

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

Step-by-step 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 = (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 = (d_A)/(1.33)`

=>
`d_A = 5 * 1.33`

=>
`d_A = 6.55 \ m`