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Mirror 4-momentum

  1. Feb 14, 2015 #1
    1. The problem statement, all variables and given/known data
    A mirror moves perpendicular to its plane with speed βc. A light ray is incident on the mirror from the “forward” direction (i.e., vm · vl < 0, where vm is the mirror’s 3-velocity and vl is the light ray’s 3-velocity) with incident angle θ (measured with respect to the mirror’s normal vector). (a) Find cos φ, where φ is the angle of reflection. (b) By what factor does the frequency of the light change upon reflection?


    2. Relevant equations

    None that I know of.
    3. The attempt at a solution
    P~ in = E c (sin θin , − cos θin , 0 , 1)
    P~ ′ in = E c [γ(sin θin − β) , − cos θin , 0 , γ(1 − β sin θin)]
    I don't know what else.
     
  2. jcsd
  3. Feb 16, 2015 #2

    Orodruin

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    What happens in the mirror rest frame when the light is reflected?
     
  4. Feb 16, 2015 #3
    In the rest frame of the mirror the angle of reflection equals the angle of incidence and there is no frequency shift.
     
  5. Feb 16, 2015 #4

    Orodruin

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    So what will be the 4-momentum of the light after reflection?
     
  6. Feb 16, 2015 #5
    Well, I went to my teacher and found the answer. But thanks for your help anyways!
     
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