A person looks horizontally at the edge of a swimming pool. If its length is 5 m, and the pool is filled to the surface, to what depth (in m) could the observer see

The observer could see to a depth of 4.38 m

Explanation:

Please check attachment for diagram.

Mathematically, from Snell law;

n1sin theta = n2 sin theta

1 * sin 90 = n2 * sin θR

where n2 = 1.33

1/1.33 = sin θR

Sin θR = 0.7519

θR = arc sin 0.7519

θR = 48.76

Now to get the height, we use the triangle

Using trigonometric ratio;

Tan( 90- θR) = H/5

H = 5 Tan( 90 - θR)

H = 5 Tan( 90-48.76)

H = 5 Tan41.24

H = 4.38 m