To see how polarized sunglasses work, it is convenient to think of light as a wave moving along a string. Just like a wave on a string, a light wave wiggles transversally to its direction of motion. And just like a wave on a string, the plane in which the string oscillates can have different orientations. For example, the oscillation can vibrate up and down, side to side or in any combination of the two directions. If the string is made to oscillate at, say, a 45 degree angle, this can be mathematically decomposed into a combination of horizontal and vertical oscillation components in equal amounts. A string oscillating at, say, 75 degrees has more vertical component than horizontal component. The angle of transverse oscillation is called the "polarization angle" (see Figure 1). By the way, when we say that a certain light source is "unpolarized" we mean that it emits waves at random angles so that on average there is no preferred direction of polarization. Direct Sunlight, light bulbs and candles are examples of unpolarized light sources. Almost no natural source of light is polarized at the source; polarization happens after some sort of interaction with matter. Therefore, for almost all sources of light, it is as though we wiggled the string in one transverse direction to generate a wavelet along the string then unpredictably changed to another transverse direction, and so on (see Figure 2). The waves come out swinging in hodge-podge polarization angles, but all travel along the direction of the string.
Figure 1: "Polarization angle" is the angle of the transverse direction of oscillation of a wave. Here, horizontal (0 degrees) and vertical (90 degrees) are shown. Angle in between can be thought of as a mixture of the two directions with different mixture ratios. The grey rectangle with a vertical slot represents a polarized filter designed to transmit the vertical oscillations of the string and block the horizontal ones. Image source: cnx.org
Figure 2: An unpolarized wave. The direction of polarization changes randomly along the wave. Sunlight and most other light sources are unpolarized but become partially polarized on reflection. Image source: astronomy.nmsu.edu
Sunlight can become partially polarized by the scattering of air molecules or by reflecting off something like a lake. This means that after scattering or reflecting the sun's waves oscillation angles, they are no longer random in all directions but have a preferred direction on average. In the case of a horizontal surface—like a lake or a road—the preferred direction is horizontal. This horizontally vibrating reflected sunlight is the nuisance we see as glare, and this is why polarized lenses are so useful to beach goers and motorists: they block glare. The polarized filters on these lenses preferentially block the horizontal component of light oscillation while transmitting the vertical component. The result is a darker image but with better contrast (see Figure 3).
Figure 3: Viewing the same scene with and without a polarizing filter. The reflected sunlight in the left image is partially polarized. The right image is taken with a filter that blocks horizontally polarized light. Image source: photography.ca/blog
The Fresnel equations quantitatively show how unpolarized light becomes partially polarized after reflection from a dielectric surface--such as water or glass. The equations are mentioned here just so the reader can see the horizontally polarized component of a wave differs in its reflection coefficient from the vertically polarized component. Unequal reflection coefficients lead to unpolarized light becoming partially polarized. Interestingly, the Fresnel equations predict the existence of an angle for which the glare is completely polarized, not just partially polarized. In other words, glare coming from this angle (known as the Brewster angle) can be completely blocked by an ideal polarizing filter. The effect is dramatic. (see Figure 4).
Figure 4: Glare reflecting at Brewster angle from a window. The light producing the glare is highly polarized allowing the polarizing filter (on the right window) to virtually remove all of it. For fresh water, the Brewster angle is about 53 degrees, so peak performance of polarized sunglasses on a calm lake happen when the sun is at an angle of about 37 degrees from the horizon (90-53= 37). Image source: boundless.com/physics
To understand how polarized sunglasses block horizontal polarization, it's important to know how the electrons in the molecules of the sunglass filter behave. Electrons are set to oscillation by the incoming light wave and therefore some of the wave energy of the light gets transferred to the electrons to be dissipated or reflected by the electrons. Polarizing filters used in sunglasses contain molecules which make it is easy for the electrons to oscillate in the horizontal direction (long direction) thus dissipating more horizontally polarized light energy. On the other hand the long molecules make it hard for electrons to oscillate in the vertical direction (short direction)—thus diminishing the electrons' dissipation of vertically polarized light waves. (see Figure 5).
Figure 5: Molecules in a polarizing filter are long in one direction and short in the perpendicular direction. Electrons can freely oscillate along the length of the molecule, absorbing or reflecting the light energy, while they are unable to oscillate very far along the short direction. The "E-field" arrows in the Figure show the direction of polarization. The small spheres labeled "e-" represent electrons. Note in the Figure how the horizontally polarized wave (top) emerges) from the its electron interaction with its amplitude reduced, while the vertically oscillating wave (bottom) comes through with undiminished amplitude. Image Source: voer.edu.vn
In practice it's difficult to get the long molecules all lined up in one direction, but somewhat lined up molecules are still effective in making a polarizer. One way to accomplish this is to put long-chain molecules on a piece of transparent stretchable material then heat and pull the stretchable material. The long molecule chains, originally in random orientations, will more or less line up in the direction of the pulling.
Figure 6 below illustrates a simplified summary of everything we just discussed about polarization: glare reducing sunglasses!
Figure 6: Polarized sunglasses block horizontally polarized light (red) but transmit vertically polarized light (blue). Image source: microscopyu.com
Ari Siletz is president of CCDMETRIX. His company specializes in automated vision system inspection and metrology. With a background in both optical and software engineering, Ari has been developing instruments for the the ophthalmic and optical coating industries since the 1980s. Writing is one of Ari's serious hobbies. He is a published author whose short stories have appeared in numerous literary anthologies. He lives in Sebastopol, California.