A transverse wave can oscillate in any plane perpendicular to its travel. A polariser lets through only one of those planes, and a second polariser then controls how much survives, following a neat cosine-squared law.
Polarisation is the restriction of the oscillations of a transverse wave to a single plane; only transverse waves can be polarised. After a first polariser, a second polariser (the analyser) transmits an intensity given by Malus law, I = I₀ cos²θ, where θ is the angle between the transmission axes. At 90° (crossed) no light gets through.
Rotate the second polariser and watch the transmitted intensity follow I = I₀ cos²θ: bright when aligned, dark when crossed at 90°.
The transmitted intensity depends on the square of the cosine of the angle.
| Angle θ | Transmitted I | Result |
|---|---|---|
| 0° (aligned) | I = I₀ | maximum |
| 60° | I = 0.25 I₀ | quarter |
| 90° (crossed) | I = 0 | none |
Four quick checks tied to this lesson. Each correct answer earns XP and lights this skill on your star map.
Polarisation is possible only for:
Unpolarised light passing through a single polarising filter becomes:
Malus law gives the intensity transmitted by a second polariser as:
When the transmission axes of two polarisers are crossed at 90°, the transmitted intensity is:
That light polarises and sound does not is a clean test of wave type.
Malus law uses cos squared, not cos: at 60° the transmitted fraction is cos²60° = 0.25, not 0.5. The angle θ is measured between the transmission axes (equivalently between the light's polarisation and the analyser axis). And remember crossed polarisers (90°) give zero, the basis of many optical switches.
Unlocks once the checks above are done. Worth more XP, written to AS Paper 1 and 2 standard.
Plane polarised light of intensity I₀ meets a polariser whose axis is at 60° to the light's polarisation. The transmitted intensity is:
Plane polarised light meets a filter with its axis at 30° to the light's polarisation. The fraction of the intensity transmitted is:
The fact that sound waves cannot be polarised is evidence that sound is:
This skill is now lit gold on your star map. You have finished the lessons of Topic 7; the Paper 1 set awaits.