Reflections from linearly vibrating objects: Plane mirror at normal incidence

The signal scattered by a moving object is traditionally evaluated by the quasistationary method. This method is not relativistically correct, although it yields satisfactory results in most practical cases. A correct approach implies solution of the problem in the accelerated reference system in which the object is at rest. The relevant Maxwell's equations, boundary conditions, and constitutive equations are derived for axes in linear sinusoidal motion. As a first application the reflections from a perfectly conducting plane in sinusoidal vibration are evaluated.