Question

Three observers $A,B$ and $C$ measure the speed of light coming from a source as $v_A,v_B$ and $v_C$. Observer $A$ moves towards the source, $C$ moves away from source and $B$ stays stationary. The surrounding medium is water. If A and C are moving at the same speed, then

• A. $v_A>v_B>v_C$
• B. $v_A<v_B<v_C$
• C. $v_A=v_B=v_C$
• D. $v_B=\frac{1}{2}(v_C+v_A)$

Answer 1

Answer: (A), (D)

The correct options are
A $v_A>v_B>v_C$
D $v_B=\frac{1}{2}(v_C+v_A)$

Speed of the light is constant with respect to any observer holds only for the vacuum. In different medium (say water) if observer is moving with respect to medium towards the source, the speed observed by the observer will be more compared to a stationary observer.
Same thing holds for a observer moving away from the source. Hence Option A.
Since they are moving at the same speed, change in speed will be same and hence Option D.
So answer is A and D.