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

  1. Mar 5, 2010 #1
    1. The problem statement, all variables and given/known data

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

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

    [tex]c\Delta t=v\Delta t+\frac{v}{f_0}[/tex]
    [tex]\Delta t = \frac{2v}{f_0(c-v)}[/tex]
    [tex]\implies t = \frac{1}{f_0} + \frac{2v}{f_0(c-v)}[/tex]
    [tex] t = \frac{1}{f_0} \left(\frac{2v+c-v}{c-v}\right)[/tex]
    [tex] \implies f=f_0 \left(\frac{c-v}{c+v}\right)[/tex]
     
  2. jcsd
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