Is there a reason that reflected light off a vertical plane has a particular polarization? I know that light reflected off the ground gets polarized (which is why polarized sunglasses help so much) but that reflection is at a steep angle and not near/at 90 degrees.
https://farside.ph.utexas.edu/teaching/em/lectures/node104.h... has a detailed derivation of dielectric reflection, but you can also skip it and just look at figure 57 at the bottom showing the predicted reflectances for the two directions of polarization depending on the incidence angle.
You're right that for perfectly vertical reflection, the polarization doesn't matter, but you're unlikely to exactly hit that. For angles between 0 and 90 degrees, light polarized parallel to the surface is always reflected better. If you perfectly hit Brewster's angle https://en.wikipedia.org/wiki/Brewster%27s_angle the light will be completely linearly polarized, but that is equally unlikely. So in general you're going to get mixed polarization that's slightly biased in one direction.
Thanks! Fun fact, do you know that apparently in reflections off a mirror, the original photon is destroyed and replaced by an "identical" one apparently?