Polarization of Light and Malus's Law

Light is a transverse electromagnetic wave, meaning the oscillating electric field associated with it always points in a direction perpendicular to the direction the wave is travelling in -- but in ordinary (unpolarized) light, coming from a source such as the Sun or an incandescent bulb, this electric field vibrates, at any instant, symmetrically in every direction perpendicular to the propagation direction, and this direction of vibration itself changes randomly and extremely rapidly, because it is the combined output of enormous numbers of independently-emitting atoms. Polarization is the process of restricting these vibrations to just one single fixed direction (perpendicular to propagation), producing what is called plane polarized light, in which the electric field vibrates only within one fixed plane, called the plane of vibration, containing the propagation direction.

A polaroid is a thin sheet material containing long-chain molecules all aligned in one common direction; it absorbs almost completely the component of an incident electric field that is parallel to these aligned chains, while freely transmitting the component perpendicular to them, called the transmission axis. Unpolarized light passed through a single polaroid (the polarizer) therefore emerges as plane polarized light, vibrating along the polarizer's transmission axis, with its intensity reduced to half the incident intensity, since on average half of the randomly-oriented incident vibration lies along the transmission axis. …