Question

Two divers jump out of their boat and swim straight down to a depth of 10 m. The water surface becomes calm again very quickly after the divers jump in. Once the divers reach their final depth they begin to swim in opposite directions at the same rate while periodically stopping to shine a flashlight back at the surface of the water where they had jumped in. After the divers have swum far enough apart they begin to notice a strong reflection from the other diver's flashlight that was not present before. How far apart are divers when this starts to happen? (n of air= 1.0, n of water = 1.33)

Please show the steps for solving this. Thank you!

Answer 1

The flash light will start thinking just after they reached critical angle(theta_c) for total external reflection of light to take place. Mu_1 sin theta_c = mu_2 sin 90 degree => 1.33 sin theta_c = 1 => sin theta_c = I/1.33 therefore theta_c = sin^-1(1/1.33) = 48.75 degree now, tan theta_c = (l/2)/n = l/2 times 10 => 1.14 = l/20 => l = 22.8 m distance between dirers