Brewster’s Law: Introduction, Derivation, Application, Angle and Relation

Brewster’s law gives the relation to find the angle of incidence of a light ray for which the reflected part of the ray is completely polarized.

Brewster law is a simple relationship between the angle of polarization and the refractive index of the medium. It states that the tangent of the polarized angle of incidence of a transparent medium is equal to its refractive index.

Brewster’s Law

According to Brewster’s law-

When an unpolarized light of known wavelength is incident on the surface of a transparent substance it experiences maximum plan polarization at the angle of incidence whose tangent is the refractive index of the substance for the wavelength.

If the tangent of the angle of incident of the incident light is equal to the refractive index of the medium then the light wave experiences maximum plane polarization.

Brewster’s Law states as –

μ = tan i

μ = Refractive Index of the Medium

i = Polarization Angle

From Snell’s Law

μ =

From Brewster’s Law

μ = tan i =

By comparing both equations

=

Cos i = Sin r = Cos ( – r )

i = – r

i+r =

This equation shows that the incident ray is perpendicular to the reflected ray.

Brewster’s Law Derivation

When unpolarized light is incident on the boundary of two medium. The wave passes into the boundary of the medium and reflected by the angle r.

For Angle of Polarization

The reflected ray will be perpendicular to the plane of incident ray and the refracted ray.

It can be written as-

i_p + 90 + r = 180

r = 90 – i_p

Snell’s Law states as-

μ =

μ =

μ = tan i_p

Application of Brewster’s Law

• The important application of Brewster’s law is the Brewster window which is a 100% light emitting glass window which is used in the gas and solid state lasers.
• Brewster’s law is used in recording a hologram.
• The other application of this law is that- By using the polarizing filter for the camera lens photographers use Brewster’s law to reduce the reflection. Polarizing filters help to take pictures of objects under the water surface.
• Polarized sunglasses are an example of Brewster’s law. In polarized sunglasses Brewster’s angle is used to reduce the glare from the Sun.
• Brewster angle microscopes are used to visualize the layers of molecules at air- liquid interface.

Brewster’s Angle

A Brewster angle is the angle where an incident beam of unpolarized light gets reflected after the complete polarization.

This is known as the Brewster angle or polarizing angle.

Formula for Brewster’s Angle is given as-

μ = tan _p

Here, μ = Refractive index of the medium.

μ =

n₂ = Absolute refractive index of first medium.

n₁ = Absolute refractive index of second medium.

tan _p =

Relation Between Brewster’s Angle and Critical Angle

Brewster’s Angle is state that = tan _p

Here, = Refractive index of the medium.

=

n₂ = Absolute refractive index of first medium.

n₁ = Absolute refractive index of second medium.

tan_p =

Critical angle is given as-

Sin = We can write this Sin_c =

From here, we get

Sin_c =

This is the relation between Brewster’s Angle and Critical Angle.

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