Polarization
Light can be plane polarized, circularly polarized or unpolarized. A plane-polarized wave has an electric field whose direction is fixed in a plane as in the previous animation. A circularly polarized wave is a superposition of an x-polarized and a y-polarized wave, where the relative phase is 90 degrees. For a circularly polarized wave moving along the z axis, the x component of the electric field wanes while the y component builds which results in the electric field's direction rotating about the z axis. By having the relative phase as +90 degress or -90 degrees, the rotation is either right-handed or left-handed. Unpolarized light is a random mixture of x- and y-polarized waves with random relative phases.
Certain materials polarize light along a certain axis due to their crystal structure. After light has passed through a polarizer, the direction of its polarization is known. If the incident wave had a polarization angle finc relative to a fixed axis and the polarizer is set at an angle fpol relative to the same fixed axis, the resultant electric field is reduced in magnitude by a factor of the cosine of the difference between these angles. The intensity of an electromagnetic wave is proportional to the square of its fields, so the polarizer reduces the intensity by the square of the cosine of that angle:
Unpolarized light can be thought of as a 50-50 mixture of two components that are polarized in perpendicular directions. When unpolarized light passes through a polarizer, one of these two components is completely absorbed, so the intensity of the light that gets through is 1/2 of the incident intensity. The light that gets through is completely polarized in the direction allowed by the polarizer.
Light from blue sky is polarized, as can be understood by thinking of it as sunlight that has been re-radiated (scattered) from charged particles in the atmosphere. "Polaroid" sun glasses and polaroid filters for cameras therefore have a striking influence on the apparent brightness of blue sky.
Light that is reflected from an insulating surface such as water or glass is polarized (more or less, depending on the angles involved), so polaroid sun glasses or camera filters have a strong and practical effect on the brightness of the reflections.
Materials whose molecules are helical, such as sugar syrup used in the lecture demonstration can produce circularly polarized light.
Tricks involving polarization are also useful for improving the information conveyed in microscope images.