Polarisation

Malus’s law and three polarisers

A polariser passes only the component of the light’s electric field along its axis. Two polarisers at right angles block everything. Put a third between them at 45° and a quarter of the light comes back: the middle one turns the polarisation so the last can pass some of it.

What you are looking at

Unpolarised light passes three polarisers at 0°, 45° and 90° and lands on a power meter.

How the bench is set up

Laser set to unpolarised, three polarisers and a power meter.

The theory

Malus’s law: light polarised at angle $\theta$ to a polariser’s axis passes with power

P = P_0\cos^2\theta.

Unpolarised light loses half at the first polariser. With polarisers at 0°, 45° and 90° the meter reads $P_0 \times \tfrac12 \times \tfrac12 \times \tfrac12 = P_0/8$ .

What to measure

I = I₀ cos²θ

Read the meter with the middle polariser at 45°: 1/8 of the laser power.
Remove the middle polariser: zero.
Turn the middle one and plot the reading against its angle: $\tfrac18\sin^2 2\theta$ at most.

What the model leaves out

The polarisers have an extinction ratio you can set; at the default a crossed pair leaks one part in 100 000.

Things to try

Add more polarisers in steps of 22.5°: more of the light survives.
Switch the laser to vertical polarisation and remove the first polariser.

References

E. Hecht (2017), Optics, 5th edition, Pearson.
É.-L. Malus (1809), Sur une propriété de la lumière réfléchie, Mémoires de physique et de chimie de la Société d’Arcueil 2, 143.

More experiments, and how the lab works, are in the laser lab’s overview.