Fresnel equations and Brewster's angle

Snell's law tells you which way a refracted ray bends, but it says nothing about how much of the light actually reflects versus how much passes through. That's the Fresnel equations' job: given the two media's refractive indices and the angle of incidence, they give the reflectance separately for light polarised parallel to the plane of incidence (the plane containing the incoming ray and the surface normal) and for light polarised perpendicular to it. At normal incidence the two agree, but as the angle grows they diverge — and the parallel component's reflectance does something the perpendicular component's never does: it passes through zero.

That zero-reflectance angle is Brewster's angle, and it has a clean geometric meaning: it's the angle at which the reflected ray and the refracted ray would be perpendicular to each other. At exactly that incidence angle, light polarised parallel to the plane of incidence can't reflect at all — physically, the oscillating dipoles in the second medium that would radiate the reflected wave are all aligned along the direction the reflected ray would have to travel, and a dipole doesn't radiate along its own axis. Perpendicular-polarised light has no such constraint and reflects at every angle, including Brewster's.

The practical consequence is that reflected light at Brewster's angle is perfectly polarised, with the relationship tan(θB) = n₂/n₁ relating the Brewster angle to the ratio of refractive indices — this is exactly how polarising sunglasses and camera filters cut glare off water and glass: most glare is sunlight reflecting near grazing angles close to Brewster's angle for that surface, and it's almost entirely polarised, so a filter oriented to block that one polarisation removes most of the glare while passing the rest of the scene largely unaffected.