Brewster’s Law describes a special condition of light reflection in which the reflected beam becomes perfectly polarized. When unpolarized light—such as sunlight or light from a lamp—hits the surface of a transparent medium like glass or water, part of the light is reflected and part is refracted. Normally, the reflected light contains electric field components vibrating in many directions. However, there exists a particular angle of incidence at which the reflected light loses all components vibrating parallel to the plane of incidence and becomes entirely polarized perpendicular to that plane. This precise angle is known as the Brewster angle.
The physical explanation arises from the interaction between the incoming electromagnetic wave and the bound electrons in the medium. When light strikes a surface, these electrons oscillate in the direction of the electric field. The oscillating charges then re-radiate light, which constitutes the reflected wave. When the refracted and reflected rays sit at a right angle to each other, the oscillating electrons cannot emit radiation in the direction of the reflected ray for certain orientations of the electric field. As a result, the reflected light contains only one polarization direction.
Brewster’s Law provides a simple mathematical relationship for the Brewster angle. If θ_B is the Brewster angle and n is the refractive index of the second medium relative to the first, then the tangent of the Brewster angle equals that refractive index. In formula form,
tan θ_B = n.
This means that the Brewster angle depends solely on the optical properties of the two media involved. For example, when light travels from air into glass with a refractive index of about 1.5, Brewster’s Law predicts a Brewster angle of roughly 56 degrees.
One striking aspect of the Brewster condition is that it occurs only for light that is linearly polarized parallel to the plane of incidence. Light vibrating in this direction cannot reflect at the Brewster angle because the boundary electrons cannot oscillate effectively to reradiate energy back into the reflection direction. Light vibrating perpendicular to the plane of incidence, however, still reflects, which is why the reflected beam becomes fully polarized.
This phenomenon has many practical applications. Polarizing sunglasses use this principle to reduce glare from horizontal surfaces such as roads or water. Because the light reflected from these surfaces tends to be polarized, lenses that block a specific polarization direction can significantly reduce brightness and improve visibility. Brewster windows, used in lasers, rely on transmitting rather than reflecting the desired polarization so that optical losses in the laser cavity are minimized. Photographers often use polarizing filters to eliminate reflections from glass and water, enhancing contrast in an image.
Overall, Brewster’s Law links the behavior of polarized light with the geometry of reflection and the optical properties of materials. Its predictive power and practical usefulness make it an essential concept in optics, illustrating how electromagnetic theory explains everyday visual effects as well as advanced technologies.