Overview: Polarisation of Light

A wave in which the vibrations of the particles of the medium are perpendicular to the direction of propagation.

A wave in which the vibrations of the particles of the medium are parallel to the direction of propagation.

The phenomenon in which the vibrations of the electric field vector of light are restricted to a single direction in a plane perpendicular to the direction of propagation.

The first crystal which polarises the light wave is called ‘polariser'. 

The second crystal which examines the nature of the light emerging from the first crystal, whether it is polarised or not, is called the ‘analyser'.

Unpolarised light is light in which the vibrations of the electric field vector occur in all possible directions in a plane perpendicular to the direction of propagation.

In plane polarised light, the vibrations of the electric vector E occur in a plane perpendicular to the direction of propagation of light, and are confined to a single direction in the plane (do not occur symmetrically in all possible directions).

The plane containing the direction of vibration of the electric vector and the direction of propagation of light is called the 'plane of vibration'.

The plane containing the direction of propagation of light and perpendicular to the plane of vibration is called the ‘plane of polarisation’.

Statement

When unpolarised light is incident on the surface of a transparent medium at a particular angle, the reflected light becomes completely plane-polarised.
This angle of incidence is called the polarising angle or Brewster’s angle (i_p).

According to Brewster’s Law, the refractive index n of the medium is related to the polarising angle by:

n = tan ⁡i_p​​

Explanation / Proof

Consider unpolarised light incident on the surface of a transparent medium (e.g., air–glass interface) at the polarising angle i_p​.

Let:

• i_p​ = angle of incidence (polarising angle)
• r = angle of refraction
• n = refractive index of the second medium w.r.t. the first

From Snell’s law:

n = \[\frac {sin ⁡i_p}{sin ⁡r}\]​​

From Brewster’s law:

n = tan⁡ i_p = \[\frac {sin⁡ i_p}{cos⁡ i_p}\]​​

Equating the two expressions for n:

\[\frac{\sin i_p}{\sin r}=\frac{\sin i_p}{\cos i_p}\]

⇒ sin r = cos i_p​

​⇒ sin r = sin(90^∘ − i_p​)

⇒ r = 90^∘ − i_p​

Hence,

i_p + r = 90^∘

Therefore, the reflected ray and refracted ray are mutually perpendicular.

Conclusion

• Brewster’s law establishes a direct relation between refractive index and polarising angle:
  n = tan⁡ i_p​​
• At the polarising angle:
  Reflected light is completely plane-polarised
  Reflected and refracted rays are perpendicular to each other
• This law explains the polarisation of light by reflection and is a strong confirmation of the transverse nature of light waves

• At the polarising angle, the reflected light becomes completely plane polarised, while the refracted light is partially polarised.
• Using a pile of parallel plates, repeated refraction and reflection produce almost completely plane-polarised light with vibrations parallel to the plane of incidence.

• Scattering of light occurs when white light passes through very small particles, such as dust or air molecules.
• The scattered light seen perpendicular to the incident beam appears blue.
• Light scattered at right angles is plane-polarised, as shown using an analyser.

Statement

The intensity of plane-polarised light transmitted through an analyser is directly proportional to the square of the cosine of the angle between the transmission axes of the polariser and the analyser.

I = I₀ cos⁡²θ

Explanation / Proof

• Let a beam of completely plane-polarised light of amplitude aaa fall on an analyser.
• Let θ be the angle between the transmission axes of the polariser and analyser.
• The amplitude of light along the analyser’s axis is a cos ⁡θ.
• Since intensity ∝ (amplitude)²,
  I = K(a cos⁡ θ)² = K a² cos⁡² θ
• If I₀ = Ka² is the incident intensity, then:
  I = I₀ cos⁡² θ

Conclusion

Thus, the transmitted intensity depends on the relative orientation of the polariser and analyser and follows the relation

I = I₀ cos⁡² θ​

This relation is known as the Law of Malus.

Polaroid is a cheap commercial device for producing and detecting plane-polarised light.

• Unpolarised light has electric vectors vibrating randomly in all directions perpendicular to the direction of propagation.
• When unpolarised light passes through an ideal polariser/analyser, the maximum transmitted intensity is 50% of the incident light.
• A Polaroid transmits only those components of light whose electric vectors vibrate parallel to its polarising direction.
• If two Polaroids are parallel, light transmitted by the first passes through the second.
• If two Polaroids are crossed (90°), no light is transmitted, showing complete extinction.

• Polaroids are used to reduce glare from shiny surfaces like wet roads and glass.
• Polarised sunglasses cut off horizontally polarised reflected light and reduce eye strain.
• Polaroids are used in car headlights and windscreens to prevent dazzling from opposite vehicles.
• Crossed Polaroids in cars block headlight glare while allowing safe visibility.
• Polaroids are fitted in microscopes to reduce glare and view minute particles clearly.
• Polaroids in camera lenses help take clear photographs of clouds by reducing scattered light.
• Polaroids are used in trains and aeroplanes to control light intensity through windows.
• Polaroid glasses are used to view three-dimensional (3D) images.
• When a Polaroid is rotated, unpolarised light shows no change in intensity.
• On rotation, plane-polarised light shows maximum and zero intensity, while partially polarised light never becomes zero.