Reflection

Light reflected from the surface of dielectric materials like glass or water is partially linearly polarized. We decompose the incident light into $\vec{E}$ components parallel and perpendicular to the plane of the paper as shown in Figure 16.8.

Figure 16.8: Polarization by reflection

To model the reflection at the surface we assume that the dielectric is a collection of dipoles which are set into oscillation by the electric field of the radiation inside the dielectric. The reflected wave is produced by the combined radiation of these oscillating dipoles. In the situation where

$$\theta_r+\theta_t=90^{\circ}$$ (16.3)

the dipole produced by the component of $\vec{E}$ parallel to the plane of the paper is aligned with the direction of the reflected wave. As a consequence the intensity of the reflected wave is zero for this component of linear polarization. The reflected wave is linearly polarized perpendicular to the plane of the paper. The angle of incidence at which this occurs is called the Brewster's angle $\theta_B$(Figure 16.9)(also known as polarization angle). This can be calculated using

(16.4)

and $\theta_t=90^{\circ}-\theta_B$ whereby

$$n_i \, \sin \theta_B = n_r \, \cos \theta_B$$ (16.5)

and

$$\tan \theta_B = \frac{ n_r}{n_i}$$ (16.6)

This is known as Brewster's Law.

Figure 16.9: Brewster's angle