H2 Physics 10 - Wave Motion and Polarisation: Malus's Law

Step 1 - Set up the problem

Unpolarised light of intensity I_0 passes through a polariser, then an analyser at 60 degrees.

Step 1 - Set up the problem

Find the intensity after each filter.

Step 1 - Set up the problem

Also find the angle for zero transmission.

Step 2 - Intensity after the polariser

An ideal polariser transmits half the intensity of unpolarised light.

Step 2 - Intensity after the polariser

It selects one polarisation component from the random mix.

Step 2 - Intensity after the polariser

Intensity after the polariser: I_0 / 2.

Step 3 - Apply Malus's law at the analyser

Malus's law: I_2 = I_1 cos squared theta.

Step 3 - Apply Malus's law at the analyser

theta = 60 degrees between the two axes.

Step 3 - Apply Malus's law at the analyser

cos 60 = 0.5, so cos squared 60 = 0.25.

Step 4 - Calculate the final intensity

I_2 = (I_0/2)(0.25) = I_0/8.

Step 4 - Calculate the final intensity

Only one eighth of the original intensity is transmitted.

Step 4 - Calculate the final intensity

That is 12.5% of the original intensity.

Step 5 - Find the angle for zero transmission

For zero transmission: cos theta = 0.

Step 5 - Find the angle for zero transmission

This happens when theta = 90 degrees - the axes are perpendicular.

Step 5 - Find the angle for zero transmission

Crossed polarisers block all light - used in LCDs and stress analysis.

Step 5 - Find the angle for zero transmission

Summary: I_0/2 after the polariser, I_0/8 after the analyser at 60 degrees, and zero at 90 degrees.