Polarisation
Polarisation
Polarisation is a property of transverse waves only. A transverse wave is polarised when its oscillations are confined to a single plane. Longitudinal waves (e.g., sound) cannot be polarised — this distinction is an important test for wave type.
Unpolarised and Polarised Light
Unpolarised light: The electric field oscillates in all directions perpendicular to the direction of travel. This is the case for light from most sources (bulbs, the Sun, flames).
Plane-polarised light: The electric field oscillates in one plane only. The plane containing the electric field vector and the direction of propagation is called the plane of polarisation.
Methods of Polarisation
1. Polaroid filters (absorption)
A polaroid filter (or polariser) is a material containing long-chain molecules aligned in one direction. It transmits only the component of the electric field oscillating in one direction (the transmission axis) and absorbs the perpendicular component.
When unpolarised light passes through a single polaroid:
- The transmitted intensity is halved: I = I₀/2
- The transmitted light is plane-polarised
2. Reflection (partial polarisation)
When light reflects off a non-metallic surface (glass, water), the reflected light is partially polarised parallel to the surface. At Brewster's angle θ_B:
tan θ_B = n₂/n₁
the reflected light is completely polarised and the reflected and refracted rays are perpendicular.
3. Scattering
Light scattered by small particles (Rayleigh scattering) is partially polarised. This is why the sky light is partially polarised — polaroid sunglasses exploit this to reduce glare.
Malus's Law
When plane-polarised light of intensity I₀ passes through a second polaroid (the analyser) whose transmission axis makes an angle θ to the polarisation direction:
I = I₀ cos²θ
| Angle θ | Transmitted intensity |
|---|---|
| 0° | I₀ (full transmission) |
| 30° | 0.75 I₀ |
| 45° | 0.50 I₀ |
| 60° | 0.25 I₀ |
| 90° | 0 (no transmission — "crossed polaroids") |
Worked Example
Unpolarised light of intensity 80 W m⁻² passes through two polaroid filters. The transmission axes make an angle of 35° with each other. Find the final intensity.
After the first polaroid: I₁ = 80/2 = 40 W m⁻²
After the second: I₂ = 40 × cos²35° = 40 × (0.8192)² = 40 × 0.6710 = 26.8 W m⁻²
Demonstrating Polarisation
Crossed polaroids experiment:
1. Place two polaroid filters in a light beam
2. Rotate one relative to the other
3. At 0° (parallel): maximum light transmission
4. At 90° (crossed): no light passes — complete extinction
5. This confirms light is a transverse wave (longitudinal waves would show no variation)
Optical Activity
Some materials (e.g., sugar solutions, quartz) rotate the plane of polarisation of light passing through them. The angle of rotation depends on:
- Concentration of the solution
- Path length through the material
- Wavelength of light
This is used in polarimetry to measure sugar concentration in the food industry and in chemical analysis.
Stress Analysis
Photoelasticity: Transparent plastic models placed between crossed polaroids show coloured stress patterns when loaded. Regions of high stress produce bright coloured fringes due to birefringence (different refractive indices for different polarisations). This technique reveals stress concentrations in engineering components.
LCD Displays
Liquid crystal displays use polarisation:
1. Light from a backlight passes through a polaroid
2. The polarised light enters a liquid crystal layer
3. With no voltage applied, the liquid crystal rotates the polarisation by 90°, allowing light through the second (crossed) polaroid — the pixel appears bright
4. With voltage applied, the liquid crystal aligns and does not rotate the polarisation — light is blocked by the crossed polaroid — the pixel appears dark
5. Varying the voltage controls the brightness of each pixel
Polarisation of Radio Waves and Microwaves
Radio waves from a dipole antenna are polarised parallel to the antenna. A receiving antenna must be aligned in the same plane to receive maximum signal. This is why TV aerials are mounted either horizontally or vertically depending on the local transmitter orientation.
Microwave polarisation demonstration: A microwave transmitter produces polarised microwaves. A metal grille acts as a polariser — it transmits microwaves polarised perpendicular to the grille bars and reflects those polarised parallel to them. Rotating the grille demonstrates Malus's law.
Importance as Evidence for Wave Nature
- Polarisation proves light is a transverse wave (resolving Newton vs Huygens debate)
- Only transverse waves can be polarised — this distinguishes them from longitudinal waves
- The polarisation of electromagnetic waves confirms that E and B fields oscillate perpendicular to the direction of propagation and perpendicular to each other