Brewster's angle, also known as the polarization angle, is the angle at which an unpolarized light beam, consisting of both horizontal and vertical polarizations, undergoes a unique phenomenon when it strikes the surface of a material with two different refractive indices. At this specific angle of incidence, the reflected light becomes horizontally polarized, while the transmitted light becomes vertically polarized. This phenomenon occurs as a result of the interaction between light and a dielectric medium, such as glass or water.

It represents the angle of incidence at which an unpolarized electromagnetic (EM) wave splits into a vertically polarized EM wave upon transmission through a surface. In this case, the reflected wave retains only the horizontal components of the incoming radiation. Conversely, when an incoming vertically polarized EM wave is incident at Brewster's angle, there is no reflection. At this specific angle, light with this particular polarization state cannot be reflected.

Brewster’s Law 

Brewster's law was named after the Scottish physicist Sir David Brewster who proposed it in 1811. It describes the relationship between light waves and the maximum polarization angle of light. According to this law, p-polarized rays completely disappear when incident on certain glasses at a specific angle. P-polarized rays are those rays in which the electric field oscillates parallel to the plane of incidence, and the light is vertically polarized.

The law states that, when an unpolarized light of known wavelength is incident on a transparent substance surface, it undergoes maximum plane polarization at the angle of incidence. This angle is defined by the tangent of the refractive index of the substance for that specific wavelength.

The angle of incidence at which the reflected light achieves complete polarization is referred to as the polarizing angle. 

The refractive index of the medium, µ, is given by,

where,

i_p is the polarizing angle

Brewster’s Angle Equation

Brewster's angle can be determined by ensuring that the reflection is zero, which can be expressed in terms of Snell's law as follows:

When θ_i=θ_B and θ_i+θ_t=90º,

Therefore,

Application of Brewster’s Law

One notable application of Brewster's angle is found in polarized sunglasses. These sunglasses utilize the principle of Brewster's angle to reduce glare caused by direct sunlight and reflections from horizontal surfaces like roads and water. By blocking horizontally polarized light, polarized sunglasses enhance visual clarity and provide a more comfortable viewing experience.

Brewster's angle is also utilized in photography. Photographers make use of polarizing filters on camera lenses to minimize reflections from highly reflective surfaces. By adjusting the filter to Brewster's angle, photographers can effectively reduce unwanted glare and capture clear, non-reflective images.

It also has application in various optical systems and devices. For example, polarizing beam splitters, optical filters, and liquid crystal displays (LCDs) leverage Brewster's angle to control the transmission and reflection of light. This allows for efficient manipulation of light polarization for specific purposes.