A point glass source is lowered from the center of the circular raft at a depth h.

A point glass source is lowered from the center of the circular raft at a depth h. at what minimum radius of the raft will the light from the source not leave the water? the refractive index of water is n

Given:
Depth h;
Refractive index n1 = n;
n2 = 1;
Find the minimum radius R;

Solution:
The light from the source will not come out of the water if total internal reflection is observed. That is, we get:
n * sin a = n2 * sin 90, where sin a = 1 / n, and a is the limiting angle of total internal reflection;
Then the minimum radius is:
R = h * tg a, where by the formula tg a = sin a / cosa;
cos a = √1 – sin ^ 2 a = √ 1 – 1 / n ^ 2 = √ (n ^ 2 – 1) / n;
Hence, R = h * (1 / n) / (√ (n ^ 2 – 1) / n) = h / √ (n ^ 2 – 1).
Answer: R = h / √ (n ^ 2 – 1).