One of the last things that we need to remember,
again you should have seen this in a physics course before,
is that when these plane waves intersect planar boundaries,
they reflect and refract.
And of course the direction of reflection and
refraction is described by Senkrecht's Law.
The amplitude, the efficiency of the light transmitting or
reflecting is given by the Fresnel Equations.
These are found from solving the electromagnetic boundary conditions
at this point or boundary for a plane wave.
They formally only apply to a plain wave.
I've copied them here so you have them for reference, and I'm going to remind you of
the sometimes confusing terminology, is that we have two possible conditions,
because we have two possible polarization states.
One is that the electric field is out of the plane of incidence.
Here I've drawn the light coming in and bouncing and
I've drawn a plane through that, the magnetic fields in the plane of incidence
and the magnetic electric field is out of the plane.
Or the opposite, the magnetic field is out of the plane and the electric field is in.
There's three different names, at least, for this.
The most common is that this is s polarization.
And that actually comes from the German for, well, as written there.
Another way, and probably the easier way to remember it, is in this polarization,
from the perspective of the electric field,
which is what we care about because we use the electric field on our wave equation.
The electric field never changes direction, it's always out of the plane.
So it could be described by a scalar
which is just the magnitude of the electric field.
Possibly positive or negative if it changes sign.
But unlike the magnetic field it's not actually changing direction.
So you can think about s as the scalar case for the electric field.
I don't actually care about the electric field direction.