Nature of Polarized Light
Light is a transverse electromagnetic wave, meaning its electric and magnetic fields oscillate perpendicular to the direction of travel. In ordinary, unpolarised light — such as sunlight or the light from a lamp — these oscillations occur in every possible direction around the axis of propagation simultaneously. Polarisation is the process by which this random mix of directions is restricted so that the electric field oscillates in only one specific plane. Understanding polarisation reveals something fundamental: light is not just a stream of energy, but a wave with a definite orientation that can be controlled. Think of a skipping rope threaded through a picket fence. If you shake the rope randomly, waves travel in all orientations, but the gap in the fence only allows vertical oscillations through — horizontal ones are blocked. A polarising filter works in exactly the same way for light, transmitting only the component of the electric field aligned with its transmission axis. The resulting light is called linearly polarised (or plane-polarised) light. This is the most common type of polarisation studied at school, though circular and elliptical polarisation also exist. Polarisation has widespread practical importance. Polaroid sunglasses reduce glare from reflective horizontal surfaces, LCD screens rely on polarised light to form images, and geologists use polarising microscopes to identify minerals. Because sound waves are longitudinal — they oscillate along the direction of travel — they cannot be polarised. Polarisation is therefore definitive proof that light behaves as a transverse wave.
- Transverse waves and oscillation planes
- What a polarising filter does
- Malus's Law: two polarisers in sequence
- Natural ways light becomes polarised
- Intensity from unpolarised light through a single polariser
Transverse waves and oscillation planes
A transverse wave has its displacement perpendicular to the direction of propagation. For light, this displacement is the electric field vector E. In unpolarised light, E points in all directions perpendicular to the ray simultaneously — you can picture countless arrows radiating outwards like the spokes of a wheel, all pointing away from the central axis.
What a polarising filter does
A linear polarising filter (such as a sheet of Polaroid material) contains long polymer molecules aligned in one direction. These molecules absorb the component of E that is parallel to them and transmit the perpendicular component. The direction perpendicular to the absorbing molecules is called the transmission axis. After passing through the filter, the light oscillates only in the plane defined by that axis — it is now linearly polarised.
Malus's Law: two polarisers in sequence
When already-polarised light strikes a second polariser (called the analyser) whose transmission axis makes an angle θ with the first, only the component of E along the analyser's axis passes through. Since intensity is proportional to the square of the amplitude, the transmitted intensity follows Malus's Law: I = I₀ cos²θ. At θ = 0° the full intensity is transmitted; at θ = 90° (crossed polarisers) the intensity drops to zero — the two filters are completely opaque together.
Natural ways light becomes polarised
Light can become polarised without a filter. Reflection from a non-metallic surface (glass, water, tarmac) partially polarises the reflected beam, predominantly in the horizontal plane — this is why polarised sunglasses with a vertical transmission axis cut glare so effectively. At a specific angle called Brewster's angle (θ_B = arctan(n), where n is the refractive index of the medium), the reflected light is completely polarised. Scattering in the atmosphere also polarises light, which is why the sky appears partially polarised when viewed at 90° to the Sun.
Intensity from unpolarised light through a single polariser
When completely unpolarised light passes through a single ideal polariser, the transmitted intensity is exactly half the incident intensity: I = I₀/2. This is because unpolarised light can be modelled as an equal mixture of two orthogonal polarisation states; the polariser transmits one and blocks the other. This factor of one-half is crucial when applying Malus's Law to situations starting with unpolarised light.
The Key Equation
- I — Transmitted intensity (W m⁻²): The intensity of light that passes through the analyser.
- I_0 — Incident polarised intensity (W m⁻²): The intensity of the polarised light reaching the analyser.
- \theta — Angle between axes (degrees or radians): The angle between the transmission axis of the polariser that created the polarised beam and the transmission axis of the analyser.
Worked Example
Problem. Unpolarised light of intensity 800 W m⁻² passes through a polariser and then through an analyser whose transmission axis is oriented at 30° to the polariser's transmission axis. Calculate the intensity of light emerging from the analyser.
Answer. The intensity of light emerging from the analyser is 300 W m⁻².
Origins · 1 minÉtienne-Louis Malus and how this was discovered
Étienne-Louis Malus discovered the polarisation of light by reflection in 1808 while looking through a calcite crystal at sunlight reflected from the windows of the Luxembourg Palace in Paris. He formulated what is now known as Malus's Law, describing how the intensity of polarised light varies with the angle of the analyser. He coined the term 'polarisation' itself, recognising that reflected light behaved as though it had distinct 'poles', analogous to a magnet. Malus made his discovery entirely by chance during an evening stroll — he happened to be carrying a calcite crystal and noticed the unexpected dimming of reflected sunlight. He died of tuberculosis at just 36, having compressed a remarkable scientific career into fewer than a decade.
Related Concepts
- Transverse and Longitudinal Waves — Polarisation is only possible in transverse waves; understanding the difference between transverse and longitudinal oscillations is essential to grasping why light can be polarised but sound cannot.
- Reflection and Refraction of Light — Brewster's angle, at which reflected light is completely polarised, arises directly from the laws of reflection and refraction and the refractive index of the medium.
- The Electromagnetic Spectrum — Light is an electromagnetic wave; recognising that all electromagnetic radiation consists of oscillating electric and magnetic fields explains the mechanism behind polarisation.
- Diffraction and Interference — Diffraction, interference, and polarisation are all wave phenomena that collectively provide compelling evidence for the wave nature of light.