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Polarisation

An unpolarised wave is a transverse wave where the direction of oscillations at any specified point of the wave are not fixed (although remaining always perpendicular to the direction of wave motion).

This means that the displacement of the wave can be in any direction (up or down or left or right).

This means that the individual oscillations of a single unpolarised wave can be in the vertical plane, horizontal plane or at any angle between both planes.

Polarisation is the process of filtering waves so that only those matching a specific pattern remain.

Polarised waves can have linear, elliptical and circular patterns. The oscillations that do not follow the pattern are effectively "filtered" out during the process.

An ocean wave is a naturally polarised wave. The water molecules only oscillate upward and downward (along a vertical axis) but not to the left and right.

Most light is naturally unpolarised.

A polariser is the device used to polarise a particular type of transverse wave (e.g. light polariser).

Longitudinal waves cannot be polarised as the oscillations of their elements are always parallel to the direction of the wave motion.

This means that all of the oscillations occur in the same plane as the direction of motion. The wave cannot be polarised without blocking the entire wave.

A circularly polarised wave is made up of two perpendicularly oriented linearly polarised waves with the same phase.
A circularly polarised wave is made up of two perpendicularly oriented linearly polarised waves with the same phase.

The amplitude $$A$$ of a linearly polarised wave after passing through a linear polariser with an axis angled at $$\theta$$ to the wave oscillations is given by: $$$A=A_{0}\cos\theta$$$ $$A_{0}$$ is the amplitude of the wave before passing through the polariser ($$A_{0}$$ is the reason why $$A$$ is used here instead of $$x_{0}$$).

Note that the wave passing through the polariser must already be linearly polarised for the equation to hold. It does not apply to all waves.

The polariser is used to change the orientation of the oscillations of the linearly polarised wave, albeit at the cost of some of its amplitude.

The intensity $$I$$ of the wave after passing through the polariser is given by (recall that $$I\propto A^{2}$$): $$$I=I_{0}\cos^{2}\theta$$$ $$I_{0}$$ is the intensity of the wave before passing through the polariser.

Change in wave intensity of a linearly polarised wave after passing through a polariser.
Change in wave intensity of a linearly polarised wave after passing through a polariser.