# Homework Help: Relativity - Doppler effect in reflection from a moving mirror

1. Mar 5, 2010

### quantumstate

1. The problem statement, all variables and given/known data

A plane mirror is moving at a uniform speed $$v$$ away from the observer and a pulsing source of light of frequency $$f_0$$.

What is the frequency of the light reflected in the mirror as seen by the observer?

This isn't an actual homework question but I have a similar question in which there is ambiguity as to whether the mirror is stationary or not. I get a different answer if the mirror moves I am hoping to comfirm that this is correct but considering this simple case.

2. Relevant equations

3. The attempt at a solution

This doesn't seem to require any special relativity with my method.

Take $$t=0, x=0$$ to be the time a pulse is received. At time $$t=\frac{1}{f_0}$$ the second pulse arrives at x=0. The second pulse catches up with the spaceship in a time given by:

$$c\Delta t=v\Delta t+\frac{v}{f_0}$$
$$\Delta t = \frac{2v}{f_0(c-v)}$$
$$\implies t = \frac{1}{f_0} + \frac{2v}{f_0(c-v)}$$
$$t = \frac{1}{f_0} \left(\frac{2v+c-v}{c-v}\right)$$
$$\implies f=f_0 \left(\frac{c-v}{c+v}\right)$$