A tube of water is traveling at ½c relative to the lab frame when a beam of light traveling in the same direction as the tube enters it. What is the speed of light in the water relative to the lab frame? (The index of refraction of water is 4/3)
A. 1/2 c
B. 2/3 c
C. 5/6 c
D. 10/11 c
E. c
A. 1/2 c
B. 2/3 c
C. 5/6 c
D. 10/11 c
E. c
(GR0177 #80)
Solution:Relativistic Addition of Velocities:
v = speed of the moving observer
u' = speed of object in the moving observer
u = speed of object in the moving observer relative to the rest observer
Given:
v = speed of water = 1/2 c
Index of refraction of water, n = c/u' = 4/3
u' = speed of light in the water = 3/4 c
u = speed of light in the water relative to the lab frame
= (1/2 c + 3/4 c) / [1 + (1/2)(3/4)]
= (5/4 c)/(11/8)
= (5/4 c)(8/11)
= 10/11 c
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