Why Do Polarized Sunglasses Work?

i-8c0e4f5fc95209bb67d3d3a39840d5f6-electric_field.jpgIn the previous post about light polarization, I promised to post an explanation of why it is that “Polarized” is a selling point for sunglasses. Given that sunlight is unpolarized, the only obvious benefit would be that polarized sunglasses will automatically block half of the light hitting them, but it’s actually much better than that. To understand why they work, though, we need to talk about how it is that light waves are produced and propagate in a medium.

Sticking with the classical picture of light as an electromagnetic wave, you can understand the production of electromagnetic waves by just looking at the electric field of a simple charged particle, like an electron. The picture at left shows the basic idea: you have some object, with some charge, and there are field lines raditating out from it in all directions (I’ve only drawn a few, to give you the basic idea).

Now, let’s imagine what happens when you suddenly move that charge some distance. When that happens, you get a picture that looks like this:

i-a21a49f08e074025dde6459484d3d26d-kinked_field.jpgIn this picture, the dotted lines represent the original field lines, and the blue lines are the field from the new position. If you’re close by the charge, everything looks more or less the same– it’s still just lines radiating out from the central point.

But we need to remember our Relativity, and recall that forces propagate at finite speed. If you’re far away from the charge, you don’t know that the charge has moved until the new lines reach you, and that takes a time equal to the distance you are from the charge divided by the speed of light. So, at large distances, you see the green field lines, which look just like the original.

Between the blue lines radiating out from the new position, and the green lines radiating out from the old position, there’s a “kink” in the electric field, shown by the red lines. This represents the transition region, during which the charge was being moved from one position to the other. That “kink” propagates outward at the speed of light, and is the beginning of a light wave. If, rather than making a single short move, you were to wiggle the charge back and forth in a regular manner, you would generate waves, moving out in all directions.

Now, look at the pattern of the “kinks.” The “kink” in the horizontal field line is rather large, but the “kink” is much smaller in the lines that go off at an angle. And if you look at the vertical line, you see that there’s no kink at all– the charge shifted exactly along the field line, so there’s no change. This is a very general result: if you shake a charged particle back and forth, you get light waves radiating out from it in every direction except along the direction of motion.

What’s this got to do with sunglasses? Well, you can think of light propagating through a medium as a wave shaking the charges in the material back and forth– the elecrons are actually bound into atoms, but they still move, and emit light. You can picture the wave that travels through the material as the sum of all those individual waves, an idea known as Huygens’s Principle— the waves emitted by the atoms makeing up the material interfere constructively in the direction of propagation, and destructively everywhere else.

Now, think about what happens when the light hits a boundary. At a boundary between two different media, you actually get two possible paths: a transmitted wave that passes into the new material (bending a bit as it enters, which is called “refraction”), and a reflected wave that bounces off the boundary and goes back out into the original medium. Both of these beams are built up from the interference of the light emitted by individual atoms.

What does this have to do with poalrization? There’s a spiffy animated applet at Davidson that demonstrates. If you shine horizontally polarized light at a surface, it will reflect and transmit no matter what angle you pick. If you use vertically polarized light, though, there is some angle at which the reflected beam from the surfacewould need to go exactly along the direction of oscillation of the wave. Which can’t happen, because the individual atoms don’t emit any light in that direction, so you only get transmitted light, and no reflected light.

That means that for any horizontal surface, there’s an angle at which vertically polarized light will not reflect. This, in turn, means that light reflecting at that angle will be horizontally polarized, even if the light source illuminating the surface is unpolarized. This is called “Brewster’s Angle” after a Scottish physicist who figured out the rule for finding the angle.

If you wear glasses made from vertical polarizers, then, light reflecting off surfaces at Brewster’s angle will be completely blocked, while light that bounced off at some other angle will get through. And light reflecting off at angles close to Brewster’s angle will be partially polarized, and thus most of it will get blocked.

This is why polarized sunglasses are particularly important for fishermen: sunlight reflecting off the surface of water will be polarized, and polarized sunglasses will block most of the glare, allowing you to see below the surface of the water more effectively. They’re also good for driving, as sunlight reflecting off the road some distance ahead will be blocked by the polarizers, reducing the strain on your eyes.

And this is why I’m looking for a new pair of polarized sunglasses that aren’t incredibly ugly– I’m going to be on vacation in the Caribbean next week, and anything that reduces the glare off white sand and blue water is a Good Thing…