7.5 Polarisation
- Syllabus
- 9702–2028–2029
- Topic
- 7.5
- Level
- AS
Learning objectives
7.5.1Polarisation is a phenomenon associated with transverse waves• understand that polarisation is a phenomenon associated with transverse waves7.5.2Malus’s law (I = I0 cos2θ ) to calculate the intensity of a plane-polarised• recall and use Malus’s law (I = I0 cos2θ ) to calculate the intensity of a plane-polarised electromagnetic wave after transmission through a polarising filter or a series of polarising filters (calculation of the effect of a polarising filter on the intensity of an unpolarised wave is not required)
Polarisation selects one transverse oscillation direction
Polarisation is the restriction of a transverse wave's oscillations to one direction perpendicular to propagation. A plane-polarised electromagnetic wave has its electric field oscillating in one fixed transverse direction.
| Wave state | Transverse oscillations |
|---|---|
| unpolarised | distributed among many directions perpendicular to propagation |
| plane polarised | restricted to one direction perpendicular to propagation |
A polarising filter has a transmission axis and transmits the component of the incident electric-field oscillation along that axis. A longitudinal wave oscillates parallel to propagation, so it has no set of transverse directions from which one can be selected; it cannot be polarised.
Rotating a filter in plane-polarised light changes the transmitted intensity and can reduce it to zero when the transmission axis is perpendicular to the incident polarisation direction. Observing polarisation is therefore evidence that a wave is transverse.
The transmission axis lies in the filter plane and specifies the transmitted oscillation direction; it is not the direction in which the wave propagates. Reduced intensity alone is not the definition of polarisation.
Apply Malus's law one filter at a time
I=I0cos2θ
I₀ is the intensity of the plane-polarised wave entering the current filter, I is its transmitted intensity, and θ is the smallest angle between the incoming polarisation direction and that filter's transmission axis.
For each filter in order: find θ from the incoming polarisation direction to the filter axis; calculate I = I₀ cos²θ; use this transmitted I as the next filter's I₀; and set the new polarisation direction equal to the axis of the filter just passed.
Vertically plane-polarised light of intensity 8.0 W m⁻² meets a first axis at 50° and a second axis at 20° to vertical. First, I₁ = 8.0 cos²50° = 3.31 W m⁻². The axes differ by 30°, so I₂ = 3.31 cos²30° = 2.48 W m⁻² ≈ 2.5 W m⁻².
| Relative angle θ | Ideal transmitted intensity |
|---|---|
| 0° | I = I₀ |
| 60° | I = 0.25I₀ |
| 90° | I = 0 |
Use cos²θ, not cos θ. For a series, θ is between the incoming polarisation and the next axis—not automatically an axis angle measured from vertical. This syllabus does not require calculating the intensity reduction when unpolarised light first enters a polarising filter; Malus's-law calculations start from a stated plane-polarised intensity.