# Malus' law

Light from an unpolarised source is allowed to fall on a piece of Polaroid P. This plane-polarises the light (it is therefore known as the polariser), which then falls on a second piece of Polaroid A. This second piece is called the analyser because it is used to analyse the polarisation of the beam from P (see Figure 1).

As A is rotated the intensity or the light emerging from it slowly changes, being a maximum at one point and a minimum after a further 90o rotation. Rotating A by another 90o will bring back a maximum once more. A theory for this was proposed by Malus in 1810.
Assume that light of amplitude Eo is incident on a piece of Polaroid which has its plane of polarisation at an angle to the direction of polarisation of the light.
Let the transmitted amplitude be E. Now E = Eo cos q, and since the intensity I is proportional to the square of the amplitude we have:

Malus’ Law:      I = Iocos2q

This is known as Malus' law. Plotting a graph of cos2q against I should give a straight line.

Student investigation
This experiment studies the polarisation of GHz waves.
Many schools have a set of apparatus that will produce and detect oscillations with a frequency of about 1 GHz (109 Hz). The wavelength of these is therefore 0.3 m.

Set up the apparatus as shown in Figure 2 and record the strength of the signal received by the receiver when it is rotated about a horizontal axis. Plot a graph of intensity against angle. It is important to avoid all unwanted reflections that might interfere with the result.