Fresnel’s equations explain the reflection of light at an interface by describing how light waves interact with a boundary between two materials that have different optical densities, such as air and glass. When light hits this boundary, part of it is reflected back into the original medium, and part of it is transmitted into the second medium. Fresnel’s equations determine how much light is reflected based on the angle of incidence, the polarization of the light, and the refractive indices of both media.
The equations take into account that light behaves as an electromagnetic wave, with electric and magnetic fields that must follow certain continuity conditions at the boundary. These conditions lead to different reflection behaviors for s-polarized and p-polarized light.
For s-polarized light, reflection increases with the angle of incidence. For p-polarized light, reflection decreases up to a certain angle (called the Brewster angle) where no reflection occurs, and then increases again beyond that angle.
Fresnel’s equations show that at normal incidence, reflection is minimal if the materials have similar refractive indices. But as the angle increases or the difference in refractive indices grows, reflection becomes more significant. These insights help explain why surfaces reflect light differently depending on viewing angle, material, and polarization.