https://farside.ph.utexas.edu/teaching/em/lectures/node104.html https://farside.ph.utexas.edu/teaching/em/lectures/node104.h... has a detailed derivation of die

https://farside.ph.utexas.edu/teaching/em/lectures/node104.html 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 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.