### Photography and Physics Tutorial: Filtering and Polarized Light

I ran across this short video on polarizing filters, Polarizing Filters for Photo and Video, and as a very amateur photographer I like tips that help me improve, but as a physicist I was a little dismayed. The presentation is some admixture of being wrong and being incomplete in terms of why the technique works. So I thought I would smooth over the errors and fill in some of the physics gaps.

The circular polarizer filter cuts out light coming from only one direction

This is either horribly watered down or misleading or just wrong, depending on your mood. The “light from only one direction” isn’t a reference to the location of the source of the light, it’s a reference to the oscillation direction of the electric field; we can view any source as being a linear combination of some amount of vertically polarized light and horizontally polarized light (or any two perpendicular axes). Unpolarized (or randomly polarized) light will have equal contributions, and polarized light will have more of one than the other; if it’s completely polarized, then it’s all one component.

If you put a linear polarizer in place with 100% linearly polarized light, it will cut down on the light according to Malus’s Law; the intensity varies as $$cos^2theta$$ using the angle between the polarizer and the light. But the narrator speaks of a circular polarizer. With circularly polarized light, the direction of the electric field changes as the light travels, so it looks like a helix (wikipedia has an animated gif). If you were looking down the path of the light, it would be a circle. (The general case is that you have the two polarization axes of arbitrary amplitude, and they are out of phase with each other. Then the E field looks like it is mapping out an ellipse, so we call this elliptical polarization).

The tutorial goes through a few examples of using the polarizer to cut down on the glare, along with a reminder that many LCD screens are sources of linearly polarized light. What’s happening in the former case is that reflected light tends to be polarized to some extent, and since that’s sunlight it tends to be bright, so you get glare. To get a good picture, you would like to preferentially reduce the brighter sources, which is why you want to put the polarizer in place as opposed to the neutral density filter, which just makes everything darker. The polarization that takes place on reflection gives you light polarized parallel to the surface, so light reflecting off of a pond or the hood of your car will be horizontally polarized to some extent (this also explains why polarizer sunglasses are useful while driving or at the beach). But light scattering off the atoms in the atmosphere is polarized as well, and that’s a little tougher to figure out, since there’s no “surface” to use as a reference. That’s where a handy tidbit from atomic physics comes in handy: in many ways atoms basically behave like little dipole antennas, and dipoles radiate perpendicular to their axis, but not along their axis. So light from the sun, which is a combination of horizontal and vertical polarization, hits some atom in the atmosphere that’s away from the line between you and the sun. The horizontal polarization looks like its electric field is pointing toward you, and that’s the direction the dipole would want to oscillate — and dipoles don’t radiate along their axis. That polarization is diminished or (at Brewster’s angle) completely gone, which means that the vertical polarization will dominate from the blue sky. Since this does depend on the angle, the filter will have a varying effect, and you can notice this especially with a wide-angle lens.

But all of the talk in the video is about circular polarizers, and as I’ve explained, the light is linearly polarized. A circular polarizer turns linear polarization into circular polarization. So why would it cut down on the amount of linearly polarized light? Here’s what the video isn’t telling you: a circular-polarizer filter for a camera is a linear polarizer and a filter to change the linearly polarized light into circularly polarized light. The linear polarizer does the job of filtering out the linearly polarized light, and then the second component (called a quarter-wave retarder) does its job and gives you the circularly polarized light. Why not just use a linear polarizer and be done with it? Because in any camera where you are seeing light that has come in through the lens (e.g. a typical SLR or video camera, rather than a camera with a separate viewer lens), the light passes through a polarization-dependent beamsplitter that sends half of the light to the viewer and the other half to the meter which tells you how much light there is (and is also important if you use autofocus). But the system expects the light to be unpolarized. If you send it linearly polarized light, there’s an excellent chance the meter will get the wrong amount of light, so the picture will be over- or underexposed (and/or blurry). Circular polarization is the next best thing as far as the meter is concerned, since all polarization directions will be present on the beamsplitter, you still get half the light sent to the meter.

Now that you have some of the physics behind it all, you can go out and use the tips in the video to take some better outdoor pictures.