Reflection of EM plane wave from a moving object

[sunjin09]

A plane wave normally incident onto a perfectly conductive surface moving in the normal direction with constant velocity comparable to the speed of light. How do I solve such problem? If I treat the conductor as static, and the source of plane wave as a moving source, do I only need to consider doppler effect, i.e., the wavelength or frequency of the plane wave is scaled, and the speed of light is unchanged?

In general, how to I solve a scattering problem with moving scatterers? Do I just treat them as time-dependent media and substitute into Maxwell's equations and figure out all the time-derivatives?

 

[Meir Achuz]

Make a Lorentz transformation to the rest system of the conducting surface or moving object. Do the scattering calculation to find the reflected fields. Then LT these fields back to the original system.

 

[sunjin09]

Make a Lorentz transformation to the rest system of the conducting surface or moving object. Do the scattering calculation to find the reflected fields. Then LT these fields back to the original system.

Thank you for replying, since I don't know Lorentz transformation (or anything about relativity), let me elaborate what I have in mind:

Assuming I'm a person standing at the conducting surface measuring EM field fluctuations, if the source of the plane wave is moving toward me, I would observe an EM fluctuation at a frequency higher than the frequency of the wave observed in the original frame, but it is still a plane wave, that's all I as well as the conductor can tell, so I can solve for the reflected field just like what I normally do. Now I go back to the original frame, recalling the source of the reflected plane wave (surface currents) is moving toward me, all I can feel is a fluctuation at a higher frequency than the ALREADY INCREASED frequency when I did my calculation in the moving frame. Does this sound about right? The frequency increases two times as a result of the Doppler effect in both forward and backward propagation, and the amplitude is unchanged?