Polarisation

When polarised light with intensity $I_0$ passes through a second polarising filter (the analyser), the intensity of the transmitted light $I$ depends on the angle $\theta$ between the transmission axes of the two filters.

This relationship is defined by Malus's Law: $I = I_0 \cos^2 \theta$

If the axes are parallel ($\theta = 0^\circ$), the intensity is at its maximum ($I = I_0$).

If the axes are perpendicular ($\theta = 90^\circ$), the intensity is zero, as the second filter blocks all oscillations allowed by the first.

Transverse vs. Longitudinal: Only transverse waves can be polarised. If a wave can be polarised, it is definitive proof that it is a transverse wave.

Unpolarised vs. Polarised Intensity: When unpolarised light of intensity $I_{total}$ passes through a single ideal polariser, the resulting intensity is always $\frac{1}{2} I_{total}$ because the average value of $\cos^2 \theta$ over all angles is $0.5$.

Identify Wave Type: Always check if the question involves sound or ultrasound. These are longitudinal and cannot be polarised; any option suggesting they can is a distractor.

The Square Factor: In Malus's Law calculations, students often forget to square the cosine. Always calculate $\cos \theta$ first, then square it before multiplying by $I_0$.

Intensity vs. Amplitude: Remember that intensity is proportional to the square of the amplitude ($I \propto A^2$). If the amplitude is reduced by a factor of $\cos \theta$, the intensity is reduced by $\cos^2 \theta$.

Sanity Check: If the angle between polarisers is $90^\circ$, the intensity must be zero. If it is $180^\circ$, the intensity returns to maximum because the axes are aligned again.

Grille Orientation: A common mistake is assuming light passes through a grille parallel to the bars (like a fence). In physics, the metal bars conduct electricity and absorb the field parallel to them, so only the perpendicular component passes.

Polarisation by Reflection: Students often forget that reflected light is polarised horizontally (parallel to the surface). This is why polarising sunglasses have vertical transmission axes to block the horizontal glare.

Single Polariser Effect: Many assume a single polariser has no effect on unpolarised light. In reality, it reduces the intensity by half and changes the wave from unpolarised to plane-polarised.