1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted