Question

A thief hides a precious jewel by placing it on the bottom of a public swimming pool. He places a circular raft on the surface of the water directly above and centered over the jewel as shown in the figure below. The surface of the water is calm. The raft, of diameter d = 8.66 m, prevents the jewel from being seen by any observer above the water, either on the raft or on the side of the pool. What is the maximum depth h of the pool for the jewel to remain unseen?

______m

Answer 1

The index of refraction of air is 1.000, and of water is 1.333.

The critical angle at the water-air boundary is q_c = Asin(1.000/1.333) = 48.6°.

To effectively hide the diamond, the raft must cover all angles less than 48.6°.

Now,

2*h*tan(theta) = diameter

h = d/2*tan /theta = 8.66/2*tan(48.6) = 3.817m