Polarization (waves)
Polarization (also polarisation) is a property applying to transverse waves that specifies the geometrical orientation of the oscillations. In a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of the wave. A simple example of a polarized transverse wave is vibrations traveling along a taut string "(see image)"; for example, in a musical instrument like a guitar string. Depending on how the string is plucked, the vibrations can be in a vertical direction, horizontal direction, or at any angle perpendicular to the string. In contrast, in longitudinal waves, such as sound waves in a liquid or gas, the displacement of the particles in the oscillation is always in the direction of propagation, so these waves do not exhibit polarization. Transverse waves that exhibit polarization include electromagnetic waves such as light and radio waves, gravitational waves, and transverse sound waves (shear waves) in solids. In some types of transverse waves, the wave displacement is limited to a single direction, so these also do not exhibit polarization; for example, in surface waves in liquids (gravity waves), the wave displacement of the particles is always in a vertical plane.
Polarizer
There is a relatively straightforward way to appreciate why a polarizer which creates a given handedness of circularly polarized light also passes that same handedness of polarized light. First, given the dual usefulness of this image, begin by imagining the circularly polarized light displayed at the top as still leaving the quarter-wave plate and traveling toward the left. Observe that had the horizontal component of the linearly polarized light been retarded by a quarter of wavelength twice, which would amount to a full half wavelength, the result would have been linearly polarized light that was at a right angle to the light that entered. If such orthogonally polarized light were rotated on the horizontal plane and directed back through the linear polarizer section of the circular polarizer it would clearly pass through given its orientation. Now imagine the circularly polarized light which has already passed through the quarter-wave plate once, turned around and directed back toward the circular polarizer again. Let the circularly polarized light illustrated at the top now represent that light. Such light is going to travel through the quarter-wave plate a second time before reaching the linear polarizer and in the process, its horizontal component is going to be retarded a second time by one quarter of a wavelength. Whether that horizontal component is retarded by one quarter of a wavelength in two distinct steps or retarded a full half wavelength all at once, the orientation of the resulting linearly polarized light will be such that it passes through the linear polarizer.