I am having a problem understanding a thing in a electrodynamics problem. Imagine we have a wall at x=0 made of a perfect conducting material. Imagine now we have an electromagnetic wave traveling perpendicular to the wall with the electric field polarized in the y direction and the magnetic field polarized in the z direction. The wave is an electromagnetic plane wave such that E=Eo cos(wt-kx). My question is when the wave hits the wall, the electrical field must be continuous at the interface between the air and the wall since it is zero on the wall it must be zero at x=0 and that gives us the condition that the reflected wave in th eplane x=0 must be Er=Eor.cos(-wt) but as far as I know there is no reason to guess what will be the dependence on x, I mean why should I assume it will be a plane wave like the incident one? Do I have any reason to believe that? Thank you for your time.