Optics Question 149
Question: A rocket is going towards moon with a speed v. The astronaut in the rocket sends signals of frequency $ \nu $ towards the moon and receives them back on reflection from the moon. What will be the frequency of the signal received by the astronaut (Take v«c)
[RPMT 1996; DPMT 2000]
Options:
A) $ \frac{c}{c-v}\nu $
B) $ \frac{c}{c-2v}\nu $
C) $ \frac{2v}{c}\nu $
D) $ \frac{2c}{v}\nu $
Show Answer
Answer:
Correct Answer: B
Solution:
In this case, we can assume as if both the source and the observer are moving towards each other with speed v.
Hence $ \nu ‘=\frac{c-u _{o}}{c-u _{s}}\nu =\frac{c-(-v)}{c-v}\nu =\frac{c+v}{c-v}\nu $
$ =\frac{(c+v)(c-v)}{{{(c-v)}^{2}}}\nu =\frac{c^{2}-v^{2}}{c^{2}+v^{2}-2vc}\nu $ Since v«c, therefore $ \nu ‘=\frac{c^{2}}{c^{2}-2vc}=\frac{c}{c-2v}\nu $
