PHYSICS:F/SCI.+ENGRS.(LL)-W/WEBASSIGN
PHYSICS:F/SCI.+ENGRS.(LL)-W/WEBASSIGN
10th Edition
ISBN: 9781337888714
Author: SERWAY
Publisher: CENGAGE L
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Chapter 38, Problem 46AP

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 + n v / c 1 + v / n c )

(b) Show that for v << c, the expression from part (a) becomes, to a good approximation,

u = c n + v v n 2

(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. (d) Evaluate u in the limit as the speed of the water approaches c.

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Chapter 38 Solutions

PHYSICS:F/SCI.+ENGRS.(LL)-W/WEBASSIGN

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