Brewster’s law

David Brewster a Scottish physicist also known as the father of modern experimental optics is remembered by physicists  for his work in Optics specially on the polarization of light.

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. μ=tanip . The angle of incidence on a transparent surface at which the beam of unpolarised  light is falling reflected back as a beam of completely plane polarised light is called Brewster angle. It is denoted by ip. The value of Brewster angle depends upon the wavelength of light it and on the essence of refracting medium. Brewster’s angle is considered valid in parallel polarization.

What is Brewster Law?

Brewster’s law is the law which gives the relation to find the angle of incidence of a light ray for which the reflected part of the ray is completely polarized. It is represented as μ=tanip.

What is Brewster angle?

Brewster angle also referred as the polarising angle as the light which gets reflected from the surface at this angle, entirely polarized perpendicular to the plane of incidence.

Polarization

Polarization is a property of electromagnetic radiation in which direction and magnitude of the vibrating electric field are related in a specified way. The plane containing the direction of vibration and the direction of wave propagation is called the plane of vibration and the plane passing through the direction of wave propagation and perpendicular to the plane vibration is called plane of polarization.  In the plane of polarization no vibrations occur. Brewster law is the polarization by reflection. 

Methods of producing plane polarised light

1. Reflection

2. Scattering

3. Double refraction

4.  Selective absorption

What are polaroids?

Polaroids are thin sheets of crystalline polarizing material which are capable of producing plane polarised light they are artificially prepared. To reduce glare of light polaroids are  used in sunglasses and camera filters,to reduce the amount of light coming from outside polaroids are also used in window panes of an aeroplane. Light from an incandescent source is unpolarised.

Brewster’s law proof

μ=tan i     [μ-refractive index ], [i = angle of polarisation]

from Snell’s law

= sin i / sin r ……1

From Brewster’s law

μ=tan i = sin i/cos i ……2

on comparing both

cos i = sin r = cos(π/2 – r)

i = π/2-r

i + r = π/2

Therefore, the reflected and the refracted rays are at right angles to each other.

Critical angle: The critical angle is the angle of incidence for which the angle of refraction is 90ᵒ.

Relationship between Brewster’s Angle and Critical Angle

Ө b = arc tan (n2/n1)

tanӨ b = n2/n1

The critical angle is given as:

Ө c = arc sin (n1/n2)

sinӨ c = n1/n2

sinӨ c = 1/(n2/n1)

But ,

tanӨ p = n2/n1

sinӨ c = 1/tanӨ b

Hene,

Өc = arc sin (1/tanӨ b)

Applications of Brewster’s law

• One of the most important applications of Brewster’s law is the Brewster window; it is a 100% light emitting glass window that is used in gas and solid state lasers.

• Photographers use Brewster’s law to reduce the reflection by using the polarizing filter for the camera lens. Polarizing filter allows photograph to take pictures of objects below the water surface

• Polarized sunglasses are also examples of Brewster’s law. Brewster’s angle is used in polarized sunglasses to reduce the glare from the Sun.

•  It is used in recording a hologram.

• Brewster angle microscopes are used  to visualise  the layers of molecules or small particles at air- liquid interface

Conclusion

With the help of Brewster law we can change unpolarised light into a polarized light.

When unpolarized light of known wavelength strike the transparent medium some of its part gets reflected and some gets refracted.  Due to Excess of one kind of vibrations, the ray which gets reflected is partially polarized. At a particular angle of incidence the reflected ray will be completely polarized that angle is known as polarizing or Brewster angle. After reflection the intensity of polarized light ray decreases because some part of the incident ray gets refracted which does not get completely polarized and has both the perpendicular and parallel components of light. Application of brewster’s law sunglasses, polarizing filter,  brewster angle microscope,  brewster window etc. Polaroids observe the path of light which produces dazzling effect in the I that’s why they are used to make sunglasses.