So the Fresnel equations can describe the reflectivity and transmission of $s$ and $p$ polarized light and show that there is a different relationship between angle of incidence and the power reflection coefficient for each type of polarization (shown in the the graph).
What i am wondering is why that is, Why is it that parallel polarization and perpendicular polarization react differently when reflecting off a medium?
Well, I encourage you to work through the derivation of the Fresnel Equations. What you’ll find is that the difference between $s$ and $p$ polarizations comes from the boundary conditions. Due to Gauss’ Law, the parallel component of the electric field is continuous across the boundary, while the normal component is discontinuous. The $p$ polarization has a component of field normal to the interface, while $s$ does not.
