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 50° with respect to the seabed. If the flashlight's beam has a divergence of 50 (i.e. the light exiting the flashlight makes a cone with an apex angle of 100) what is the height of the beam when it shines on the cabin of the boat? Will crew member's 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 2. n-1.339 20 m (10) You are examining the surface of a glass slab and notice a scratch. Changing the height of the microscope to change position of the focal point, you find that you are able to see the scratch in focus twice. Once with the microscope focused on the surface of the glass, and once with the microscope shifted 5 mm closer to the surface. What is the cause of the second image? Draw a ray diagram to help you explain. The thickness of the glass slab is 4 mm. What is the refractive index of the glass slab assuming the medium between the microscope and the slab is air (n#1) 3. (10) When light passes through a rectangular plate with parallel top and bottom surfaces, the exiting ray propagates parallel to the incident ray, but it is displaced. Show that this displacement, s, is equal to 4. d sin(θ1-θ2) cos 02 where θ1 and θ2 are the angles of incidence and refraction respectively and d is the plate thickness. How much is the displacement when the plate has an index of refraction of 1.8 and a thickness of 5 cm, the plate is sitting in air (n1), and the angle of incidence is 60.

Answer 1