Why does circular polarization handedness reverse at normal incidence reflection?

[MMS]

Hello everyone,

I was just reading on circular polarization on Wikipedia and came across the sentence "The handedness of polarized light is also reversed when it is reflected off of a surface at normal incidence".
I can see that the circular polarized wave should propagate in the opposite direction but I can't see how the polarization changes. I'd be happy to get an explanation or as to how this can be proven (say, mathematically).

Thanks in advance.

https://en.wikipedia.org/wiki/Circular_polarization

 

[andrewkirk]

Consider a circularly-polarised beam propagating towards a mirror in a direction perpendicular to the mirror. Assume the polarisation is clockwise when looking towards the mirror, and if we think of the beam as a cylinder we can visualise that as a red arrow at the top of the cylinder pointing to the right as we look at the mirror.

The wave reflects and starts coming back towards us. The red arrow is still pointing to the right and so still indicates a clockwise rotation from our point of view if we are still looking towards the mirror (so the beam is now heading towards us).
But now our point of view, relative to the direction of the wave, is opposite to what it was previously. So the clockwise rotation we see from our viewpoint means there is an anti-clockwise rotation from the viewpoint of somebody standing behind the beam and looking forwards through it.