# M7-S7: Polarisation of Light

#### What is polarisation?

• Electromagnetic waves possess electric and magnetic fields which oscillate perpendicular to each other. However, these fields can be orientated in infinitely many axes – as long as the two fields remain perpendicular. The axis along which the electric field oscillates is referred to as the polarisation axis.
• When a light wave possesses many different polarisation axes, it is
• When a light wave possesses only one polarisation axis, it is polarised.

Unpolarised light can be transformed into polarised light

• A polaroid filter is able to polarise light because of its chemical composition. The structure of the filter is arranged in a way such that only light with a particular polarisation axis can pass through.

The chemical composition of polaroid filters produces a specific transmission axis for light waves. The intensity of light that is allowed to pass through the filter depends on the angle between the filter and wave’s polarisation axis.

This can be better understood using the Picket Fence analogy. Light as an electromagnetic wave has oscillating electric and magnetic fields. Polaroid filters exploit the plane of these oscillation by only letting waves whose electric fields parallel to the transmission axis of the material.

Malus’ Law quantitatively characterises this relationship between axis angle and light intensity transmitted or blocked.

#### Deriving Malus' Law

In the diagram below, the first polaroid filter has a vertical transmission axis which only permits light with a polarisation axis of the same orientation to pass through.

Figure 1

Suppose we have a second piece of polaroid whose transmission axis makes an angle θ with that of the first one. The E vector of the light between the polaroids can be resolved into two components, one parallel and one perpendicular to the transmission axis of the second Polaroid (see Figure 1). If we call the direction of transmission of the second polaroid y’,

Where Ey’ and Ey are the amplitude of the electric field of light passing through polaroid y’ and y respectively.

The intensity of a wave is directly proportional to the square of its amplitude.

Therefore,

Where I and I0 are intensities of light before and after passing through a polariser. θ is the angle between the transmission axis of the polariser and the light’s polarisation axis before entering the polariser.

Calculation Example

An incident, unpolarised natural light passes through three sequential polarisers (polaroid) with each orientated at a specific angle as shown.

What intensity as a percentage of the light after polariser 1 passes through polariser 2?

Let I0 be the initial intensity (after polariser 1) and I1 be the intensity after polariser A:

Let I2 be the intensity passing through polariser:

Therefore, 25% of the incident light passes through polariser 2

#### Experiments involving polarisation supported Huygens’ wave model

Polarising filters have a unique molecular structure that allows only light having a single orientation to pass through.

If a beam of light is allowed to impact a polariser, only light rays oriented parallel to the polarising direction are able to pass through the polariser. If a second polariser is positioned behind the first and oriented in the same direction, then light passing through the first polariser will also pass through the second.

However, if the second polariser is rotated at a small angle, the amount of light passing through will be decreased. When the second polariser is rotated so the orientation is perpendicular to that of the first polariser, then none of the light passing through the first polariser will pass through the second.

This effect is easily explained with the wave theory, but no manipulation of the particle theory can explain how light is blocked by the second polariser.

The effects observed with polarised light were critical to the development of the concept that light consists of transverse waves having components that are perpendicular to the direction of propagation. Each of the transverse components must have a specific orientation direction that enables it to either pass through or to be blocked by a polariser. Only those waves with a transverse component parallel to the polarising filter will pass through, and all others will be blocked.

Previous section: Particle and Wave Model of Light

Next section: Quantum Theory