# Interaction of electromagnetic waves with a plane mirror

1. May 5, 2013

### Jimmy87

I was reading about how a plane mirror reflects light and would like confirmation I have the right theory. It says that the metal coating of a mirror is a conductor in electrostatic equilibrium which means the electric field is zero. As the electromagnetic wave hits the mirror the electrons re-arrange themselves to keep the electric field zero. The only way to do this is reflect the light back. If we were to set up some kind of situation so as to induce a current on the surface of the mirror (by connecting some kind of power source) what would then happen to the incoming light since we would now have an electric field. My maths is not brilliant so please don't throw lots of equations at me.

2. May 5, 2013

### sophiecentaur

A thought experiment involving radio waves might be easier to get to grips with. Imagine a set of radio antennae, in a row, in the path of a radio wave (a plane wave, to make it easier) which arrives at an angle. The signals arriving at each of these antennae would all be the same except for their phases (because the wave arrives at slightly different times for each antenna). Now imagine making a recording of each of the received signals and then replaying it in antiphase (keeping things perfectly synchronised). The signals from all of the antenna would radiate out in all directions but, in all directions but one, they would add up (interfere) to give zero resultant. The only direction that any resultant would be formed would be in the direction of what we'd usually call the 'reflected' wave (i.e. symmetrically about the Normal to the plane of the line of the antennae. Replacing the individual antennae with a sheet of metal, the currents induced in each part of the sheet would, in fact, be such as to generate equal and opposite re-radiated waves (wavelets) from each point. This will produce radiation only in one direction - again, because there is destructive interference in all other directions.
Replace radio waves with light and scale things down 'a bit' in size and the same argument applies.
No Maths - OK?