understand that polarisation is a phenomenon associated with transverse waves

Cambridge A-Level Physics 9702 – Polarisation

Polarisation

1. What is polarisation?

Polarisation is a property of transverse waves in which the direction of oscillation of the wave’s field vector is restricted to a particular orientation.

2. Why only transverse waves can be polarised

In a longitudinal wave the oscillations are parallel to the direction of propagation, so there is no independent direction that can be selected. In a transverse wave the oscillations are perpendicular to the direction of travel, providing a plane in which the direction can be fixed.

3. Types of polarisation

Type Oscillation pattern Key characteristics
Linear Oscillation occurs in a single plane Electric field vector remains in a fixed direction
Circular Electric field rotates at constant magnitude, tracing a circle Phase difference of $90^\circ$ between orthogonal components
Elliptical General case; tip of the field vector traces an ellipse Arbitrary phase difference and amplitude ratio

4. Polarisation of electromagnetic (EM) waves

EM waves consist of mutually perpendicular electric ($\mathbf{E}$) and magnetic ($\mathbf{B}$) fields that are both transverse to the direction of propagation $\mathbf{k}$. The polarisation of an EM wave is defined by the direction of its electric field vector.

5. Producing polarised light

  • Polarising filters: Materials with aligned molecules absorb one component of the electric field, transmitting the orthogonal component.
  • Reflection: At Brewster’s angle, reflected light is linearly polarised with the electric field perpendicular to the plane of incidence.
  • Scattering: Rayleigh scattering preferentially transmits light polarised perpendicular to the scattering plane, giving the sky its polarisation pattern.

6. Quantitative description – Malus’s Law

When linearly polarised light of initial intensity $I_0$ passes through a second polariser (analyser) whose transmission axis makes an angle $\theta$ with the incident polarisation direction, the transmitted intensity $I$ is

$$I = I_0 \cos^2\theta$$

This relationship is fundamental for experiments that measure the degree of polarisation.

7. Example calculation

If $I_0 = 100\ \text{W m}^{-2}$ and the analyser is set at $\theta = 30^\circ$, the transmitted intensity is

$$I = 100 \cos^2 30^\circ = 100 \times \left(\frac{\sqrt{3}}{2}\right)^2 = 75\ \text{W m}^{-2}.$$

8. Applications of polarisation

  1. Reducing glare in sunglasses and camera lenses.
  2. Liquid crystal displays (LCDs) – control of light transmission.
  3. Stress analysis in transparent materials using polariscope.
  4. Optical communication – polarisation multiplexing to increase bandwidth.
Suggested diagram: A ray of unpolarised light incident on a polarising filter, showing the transmitted electric field vector aligned with the filter’s transmission axis.

9. Key points to remember

  • Only transverse waves can exhibit polarisation.
  • Linear, circular, and elliptical are the three ideal states of polarisation.
  • Malus’s law quantifies how the intensity of linearly polarised light changes with the relative angle between polariser and analyser.
  • Polarisation is exploited in many modern technologies, from eyewear to displays and optical sensors.