For a conducting sheet that is transverse to a constant uniform incident field, I believe the resulting total field would simply be the incident field doubled. I'm trying to figure out why this happens, preferrably avoiding the method of images since I am using this to figure out how the method of images works. What I have so far: The incident field will push positive charges in the sheet in the same direction that the incident field is pointing, and pull the sheet's negative charges opposite to the direction the incident field is pointing. It's clear from this that the sheet's presense will strengthen the field, but how do you know how much it strengthens the field? It seems to me that as long as the field due to the conducting sheet is transverse to the surface of the sheet, it is consistent with gauss's law, regardless of the magnitude.