Plane EM Waves: Polarization States Explained for School

A plane electromagnetic wave is an idealised wave whose electric field has the same phase over any flat plane perpendicular to its travel direction. Polarisation describes how the tip of the electric field vector moves as the wave passes a fixed point.

Polarisation is not a minor detail. It controls glare, LCD displays, radio antenna alignment and many laser experiments, so school physics treats the main states carefully.

Key Concepts

In linear polarisation, E vibrates along one fixed line. In circular polarisation, the E tip traces a circle, formed by two perpendicular components of equal amplitude with a phase difference of 90 degrees. In elliptical polarisation, the tip traces an ellipse, the general case. Unpolarised light contains many waves with random linear directions. A polariser transmits only the component of E along its transmission axis. The magnetic field follows E, staying perpendicular to both E and the propagation direction.

Formulas

For linear polarisation after a polariser, Malus law: I = I0 cos^2 θ, where I0 is intensity before the polariser in W/m^2, I is transmitted intensity, and θ is the angle between the incoming polarisation and the polariser axis. For unpolarised light through one ideal polariser, I = I0/2. Component form for a wave along z: E = E0x cos(kz - ωt) x̂ + E0y cos(kz - ωt + φ) ŷ. Equal amplitudes with φ = 90 degrees give circular polarisation; unequal amplitudes or other φ give elliptical.

Worked Example

Linearly polarised light of intensity 80 W/m^2 passes through a polariser whose axis is 30 degrees to the polarisation direction. Find transmitted intensity. Step 1: Use Malus law I = I0 cos^2 θ. Step 2: cos 30° = 0.866, so cos^2 30° = 0.75. Step 3: I = 80 × 0.75 = 60 W/m^2. Step 4: If instead the incoming light were unpolarised at 80 W/m^2, the first polariser would transmit 40 W/m^2 regardless of its rotation angle.

Common Misconceptions

• Polarisation refers to the electric field direction by convention, not the magnetic field.
• Circularly polarised light is not unpolarised. Its E vector rotates regularly with a definite handedness.
• Sunglasses do not simply make light dimmer. Polarised lenses preferentially block horizontally polarised glare from roads and water.

Real-World Applications

• Polarised sunglasses and camera filters reduce reflections and improve contrast.
• LCD panels twist and select polarisation to make pixels bright or dark.
• Satellite and radio links choose polarisation to separate channels and match antennas.

Plane waves may be linearly, circularly or elliptically polarised depending on the two perpendicular E components and their phase difference. Malus law quantifies what a polariser transmits, linking theory to displays and glare control.