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?