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View submission: Ask Anything Wednesday - Physics, Astronomy, Earth and Planetary Science
Photons propagate at the speed of light, which is constant in any inertial frame of reference. So, no.
You can find the frequency change in the original frame of reference by considering that a mirror moving toward a light source will hit the next wave slightly faster than the previous one, and the outgoing waves have to match the incoming ones. (i.e., this is a boundary condition). It's a simple linear equation, the equivalent of "a train leaves Pittsburgh at 10:00 a.m. traveling toward Cleveland at 60 mph and another leaves Cleveland at 10:15 traveling toward Pittsburgh at 50 mph" type of problem.
There's nothing here!