Reflectivity of polarized light

The reflection of a polarized beam of light from a dielectric material such as glass was described by Augustin Jean Fresnel in 1823. While his derivation was based on an elastic theory of light waves, the same results are found with electromagnetic theory. The ratio of the reflected intensity to the incident intensity is called the reflectivity of the surface. It depends on the polarization of the incident light wave. Let $\theta_i$ be the angle of incidence and $\theta_t$ be the angle of transmission. Snell's law relates these according to

$$n sin(\theta_t) = sin(\theta_i)$$ (21)

The reflectivity for light polarized in (parallel to) the plane of incidence is

$${\cal R}_\parallel = {tan^2\left(\theta_i - \theta_t\right)} / {tan^2\left(\theta_i + \theta_t\right)}$$ (22)

but for light polarized perpendicular to the plane of incidence it is

$${\cal R}_\perp = {sin^2\left(\theta_i - \theta_t\right)} / {sin^2\left(\theta_i + \theta_t\right)}$$ (23)

Notice that if the light is polarized in (parallel to) the plane of incidence the denominator of the right hand side will be infinite when the sum $(\theta_i+\theta_t) = 90^\circ$. The angle of incidence when this happens is called Brewster's angle. For light polarized in the plane of incidence, no energy is reflected at Brewster's angle.