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Question
Three observers A, B and C measure the speed of light coming from a source to be νA, νBand νC. A moves towards the source and C moves away from the source at the same speed. B remains stationary. The surrounding space is water everywhere.
(a) \[\nu_A > \nu_B > \nu_C\]
(b) \[\nu_A < \nu_B < \nu_C\]
(c) \[\nu_A = \nu_B = \nu_C\]
(d) \[\nu_B = \frac{1}{2}\left( \nu_A + \nu_C \right)\]
Solution
(a) \[\nu_A > \nu_B > \nu_C\]
(d) \[\nu_B = \frac{1}{2}\left( \nu_A + \nu_C \right)\]
In any other medium, the speed of light is given by \[v = c/\eta,\] where \[\eta \] is the refractive index of the medium and according to Doppler effect, for an observer moving towards the source ,speed of light appears to be more than the other two cases. On the other hand, it will be least when the observer is moving away from the source.
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