The motion of a transparent medium influences the speed of light. This effect was first observed by Fizeau in 1851. Consider a light beam in water. The water moves with speed v in a horizontal pipe. Assume the light travels in the same direction as the water moves. The speed of light with respect to the water is c/n, where n = 1.33 is the index of refraction of water. (a) Use the velocity transformation equation to show that the speed of the light measured in the laboratory frame is u = c/n( 1 + nv/c/1 + v/nc ). (Do this on paper. Your instructor may ask you to turn in this work.)
(b) Show that for v c, the expression from part (a) becomes, to a good approximation, u=c/n + v-v/n2 (Do this on paper. Your instructor may ask you to turn in this work.)
(c) Argue for or against the view that we should expect the result to be u = (c/n) + v according to the Galilean transformation and that the presence of the term -v/n2 represents a relativistic effect appearing even at "nonrelativistic" speeds. This answer has not been graded yet.
(d) Evaluate u in the limit as the speed of the water approaches c. (Use the following as necessary: c.)