understand that polarisation is a phenomenon associated with transverse waves

Published by Patrick Mutisya · 14 days ago

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

TypeOscillation patternKey characteristics
LinearOscillation occurs in a single planeElectric field vector remains in a fixed direction
CircularElectric field rotates at constant magnitude, tracing a circlePhase difference of \$90^\circ\$ between orthogonal components
EllipticalGeneral case; tip of the field vector traces an ellipseArbitrary 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.