Question

(15) A diver has decided to go for a night dive. Unfortunately, the crew of another small dive boat has ignored the warning floater and decided to drop an anchor in the immediate vicinity. While the diver was distracted by marine life, the diver’s foot was pinned under the anchor and wedged against a rock. To escape, the diver must signal an SOS to the boat above using a powerful, but narrow beam, dive light. The diver’s depth gauge reads 15 m. By virtue of a light breeze the boat has blown such that the diver estimates the bow is 20 m downwind of the anchor. The diver guesses (correctly) the height of the boat deck, plus the height of the typical crew member is 4 m above the water. Using this guess work the diver decides to shine the light at an angle of 50º with respect to the seabed. If the flashlight’s beam has a divergence of 5° (i.e. the light exiting the flashlight makes a cone with an apex angle of 10°) what is the height of the beam when it shines on the cabin of the boat? Will crew members have a chance to see the light? The refractive index of salt water is ~1.339. Neglect dispersion. Assume that the medium above the water is air.

Answer 1