Mirror 4-Momentum: Find Frequency Change on Reflection

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Homework Statement


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?

Homework Equations



None that I know of.

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.
 

Discussion

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What happens in the mirror rest frame when the light is reflected?
 
In the rest frame of the mirror the angle of reflection equals the angle of incidence and there is no frequency shift.
 
So what will be the 4-momentum of the light after reflection?
 
Well, I went to my teacher and found the answer. But thanks for your help anyways!