When P-polarized light is incident on an elliptical metallic reflector, is the polarization of the reflected light unchanged or is it randomly polarized?

When polarized light is incident on a conductive surface like a metallic coating, a 180° phase factor gets added to the beam. If you start with linear polarized light, this rotates the polarization direction from θ to θ +180° which is the same linear polarization direction. Circular polarization, which can be defined as two equal linear states with 90° phase difference between them, undergoes a more obvious change. 180° is added to the phase difference and it becomes 270° (or -90°). This means the linear state that was leading is now lagging the other (orthogonal) piece by a quarter wave.