Malus's Law

Malus’s law tells you how much of a beam of linearly polarised light gets through an analyser (a second polarising filter) when their transmission axes are at an angle. The bcos^2 factor comes from resolving the electric field into the component aligned with the analyser: the transmitted field amplitude scales as cos, and intensity is proportional to the square of field amplitude, so the result is cos^2. It applies to ideal polarisers and a perfectly linearly polarised incident beam.

Use this when analysing polarised-light experiments, such as rotating an analyser to measure polarisation angle or transmitted intensity. It is also useful in optics problems involving polarising sunglasses, LCDs, stress analysis with polarised light, and any setup with two linear polarisers.

• Using cos instead of cos^2 for intensity, forgetting that intensity depends on the square of the field amplitude
• Measuring  from the wrong reference direction, such as the surface normal instead of the polarisation axis
• Applying the law to unpolarised light without first accounting for the 50% loss at an ideal first polariser