How are polarisation and wave direction related in transverse waves?

In transverse waves, the direction of polarisation is perpendicular to the direction of wave propagation.

In more detail, transverse waves are a type of wave where the oscillations or vibrations are at right angles to the direction of the wave's travel. This is in contrast to longitudinal waves, where the oscillations are in the same direction as the wave's travel. Examples of transverse waves include light waves, radio waves, and seismic S-waves.

Polarisation is a property of waves that describes the orientation of their oscillations. For transverse waves, this can be thought of as the direction in which the waves 'wiggle'. If the direction of these oscillations is fixed, the wave is said to be linearly polarised. If the direction of oscillation changes or rotates, the wave is said to be circularly or elliptically polarised.

The relationship between polarisation and wave direction in transverse waves is that the polarisation is always perpendicular to the direction of wave propagation. This means that if you were to look at a transverse wave moving towards you, the polarisation would be the direction in which the wave is 'wiggling' from side to side.

For example, consider a light wave travelling from a distant star to your eye. The direction of wave propagation is from the star to your eye, and the polarisation is the direction in which the electric field of the light wave is oscillating. This could be up and down, left and right, or at any angle in between, but it will always be at right angles to the direction from the star to your eye.

This relationship is a fundamental property of transverse waves and is a direct consequence of how they are generated and propagate. It is also the basis for many technologies and scientific techniques, such as polarised sunglasses, which work by blocking light waves that are polarised in a certain direction, and polarimetry, which is used to measure and analyse the polarisation of light.