Free How to Teach Physics to Your Dog by CHAD ORZEL Page A

in-between angle is like a bunny that’s zigzagging left and right, while also hopping up and down?”
    “Yes, that’s right.”
    “Or a squirrel that’s jumping up and down while it zigzags left and right?”
    “I think that’s about enough prey examples for now.”
    “You’re no fun.”
    Thinking of in-between polarizations as a sum of horizontal and vertical components is a useful trick because it makes it easy to see what happens when light encounters a polarizing filter. Polarizing filters are devices that will allow light polarized at a particular angle—vertical, say—to pass through unimpeded, while light polarized at an angle 90° away—horizontal—will be completely absorbed. You can understand the effect by imagining a dog on a leash that passes through a picket fence. If you shake the leash up and down, the wave will pass right through, but side-to-side shaking will be blocked by the boards of the fence.
    When light at an angle between vertical and horizontal strikes a vertically oriented polarizing filter, only the vertical component of the light will pass through. This lowers the intensity ofthe light on the other side, by an amount that depends on the angle. For small angles, most of the light makes it through—at an angle of 30°, the beam on the far side is three-fourths as bright as the initial beam—while for larger angles, most of the beam is blocked—at 60° from vertical, the beam on the far side is only one-fourth as bright as the initial beam. At an angle of 45°, midway between horizontal and vertical, exactly half of the light will pass through the filter.
    The light on the far side of the filter is polarized at the angle of the filter, no matter what angle it started at. For this reason, polarizing filters are commonly called polarizers: light passing through a vertically oriented polarizing filter will emerge as vertically polarized light, whether it started with vertical polarization or at some other angle. The overall amount of light will be different, but the polarization will be the same. All of the light passing through a vertically oriented filter will pass through a second vertical filter, and all of it will be blocked by a horizontally oriented filter.
    “What is all this good for, anyway?”
    “Other than helping demonstrate quantum physics? Plenty. Light polarization is an extremely useful thing. Digital displays on watches, cell phones, and televisions use a polarizer in front of a light source to vary the amount of light that gets through. And polarizing filters are also used to make sunglasses.”
    “Sunglasses?”
    “Yeah, those sunglasses that I wear when I take you for walks are actually polarizing filters. The light from the sun is unpolarized—it’s as likely to be horizontal as vertical—but when light reflects off a surface, it tends to become slightly polarized. Light reflecting off the road out in front of us when we’re walking has more horizontal polarization than vertical, so by wearing vertical polarizers as sunglasses, I can block most of that light.”
    “What’s the point of that? Doesn’t it make it harder to see?”

    “Actually, it reduces the glare off the road, and makes it easier to see things up ahead.”
    “Things . . . Like bunnies in the road?”
    “For example, yes.”
    “Can I have some polarized sunglasses so I can see bunnies?”
    “The ones I have won’t fit on your ears, but we’ll look into it. Later. First, I have to talk about quantum measurement with polarized light.”
    “Oh, yeah. Quantum physics. Right.”
    How does all this apply to light as a particle, though? We spent a good chunk of chapter 1 describing how a beam of light is both a stream of photons and a smooth wave. The last few pages have been discussing polarization in classical terms. How do we handle light polarization in quantum physics?
    When we’re dealing with classical light waves, it’s easy to understand how part of a wave can pass through the