# Brewster’s Law

### Brewster’s Law

Brewster’s law is a relationship of light waves at the maximum polarization angle of light. This law is named after Sir David Brewster, a Scottish physicist, who proposed the law in the year 1811. The law states that the p-polarized rays vanish completely on different glasses at a particular angle.

Further, the polarization angle is also called as Brewster’s angle. It is an angle of incidence where the ray of light having a p-polarization transmitted through a dielectric surface that is transparent without any reflection. While, the unpolarised light at this angle is transmitted, the light is reflected from the surface.

Brewster was able to determine that the refractive index of the medium is numerically equal to the tangent angle of polarization.

μ = tan i

Where,

μ = Refractive index of the medium

i = Polarization angle

From Snell’s Law:

$$\mu \,\,=\,\frac{\sin \,i}{\cos \,i}$$ … (1)

From Brewster’s Law:

$$\mu \,\,=\,\tan \,i\,=\,\frac{\sin \,i}{\cos \,i}$$ … (2)

Comparing both formulas (1) and (2)

$$\cos \,i\,=\,\sin \,r\,=\,\cos \,\left( \frac{\pi }{2}\,-\,r \right)$$,

$$i\,=\,\frac{\pi }{2}\,-\,r$$ (Or) $$i\,+\,r\,=\,\frac{\pi }{2}$$,

As, i + r = π/2 < ABC is also equal to the π/2 therefore, the reflected and the refracted rays are at right angles to each other.

Application of Brewster’s Law: One general example for the application of Brewster’s law is polarized sunglasses. These glasses uses the principle of Brewster’s angle. The polarized glasses reduce glare that is reflecting directly from the sun and also from horizontal surface like road and water. Photographers also use the same law to reduce the reflection from reflective surfaces by using polarizing filter for the lens.Brewster’s LawBrewster’s Law.