Polarisation and Malus’ Law – Learn

Polarisation of light occurs when light is allowed to oscillate in one direction only. Light from sources such as a light globe and the sun are unpolarised – they have light waves which oscillate in every direction or plane. The polarisation of light was further evidence which supported Huygen’s theory on light as only transverse waves can be polarised.

The diagram below illustrates the polarisation of light. Light from an unpolarised source is polarised in the vertical plane by the vertical polarising filter. 

If light that is polarised in one plane passes through a polarising filter perpendicular to the source, no light will be transmitted. This is illustrated in the diagram below:

A special case occurs when the light wave is at an angle to the filters axis which is not 90º. If a polarised wave has an axis at an angle different to the filter’s axis, only the vertical component of the wave is passed through. The result is that the intensity of the light passing through the filter will be less than the intensity of the original light.

This phenomenon can be observed when light is passed through a double filter arrangement. The first filter is known as the polariser and the second filter is known as the analyser (this is illustrated in the diagram above). The intensity of light passing through the analyser is determined using Malus’s Law:

I={ I }_{ 0 }\cos ^{ 2 }{ \theta }

where:

I is the intensity of the emerging polarised light (in cd)

{ I }_{ 0 } is the intensity of polarised light falling on the analyser (in cd)

\theta is the angle between the axis of the incident polarised light and the axis of the analyser

Example:

Polarised light with an intensity of 100cd passes through a analysing filter at an angle of 35° to the plane of the incident light. Calculate the intensity of the light as it passes through the polarising filter:

Answer:

using: I={ I }_{ 0 }\cos ^{ 2 }{ \theta }

I=100\cos ^{ 2 }{ 35 }

I=67.1\;cd