Brewster's angle

created by ilteroi

(idea) by ilteroi (1.3 wk) (print) ? 1 C! I like it! Tue Feb 11 2003 at 23:09:59

A special angle of reflection at which both the reflected and refracted ray are completely polarized.

To elaborate:
Light consists on the one hand of particles called photons, but it can also behave like a wave. (See wave-particle dualism). Such a wave has not only a direction of propagation, but also a direction in which it is oscillating, its polarization vector. (Actually this is the electromagnetic field vector which is perpendicular to the propagation vector, and perpendicular to both of them is the magnetic field vector, but that one isn't talked about much because if you know the former two you can always calculate the latter.)

Anyway, light is emitted by oscillating dipoles (basically little sticks with electrical charge running up and down). The direction of this oscillation defines the polarization of the emitted wave. Therefore we know that a dipole cannot emit radiation in the direction of its axis, because polarization and propagation have to be perpendicular to one another!

Because there are many many many unordered dipoles in a common lightbulb (as well as in the sun), our normal light contains all sorts of different waves with all sorts of polarization, it is so to speak unpolarized. Light containing only waves with one and the same direction of polarization on the other hand is called polarized. (Note that there is also circular polarized light, but that's more of a gimmick.)

For a wave to be reflected means to be absorbed by a dipole and then to be re-emitted. Imagine yourself looking down the axis of propagation of a ray of light that hits the surface of a lake at an angle of say 53 degrees (the significance of that number will be explained later). If the polarization of the wave is neither horizontal nor vertical (in your personal coordinate system) we will split it in two, one horizontally polarized, the other vertically (the wonders of vector arithmetics).

The dipoles (water molecules) now can be induced by the two waves to oscillate horizontally and vertically. Because the dipoles oscillating vertically have their axis exactly in the direction the reflection ray is going to head, they cannot contribute to it. Instead our reflected ray is made up completely of the emissions of the horizontally oscillating molecules, it is horizontally polarized, qed. (Note that the refracted ray will be vertically polarized to make up for it.)

53 degrees is Brewster's angle for air and water (it depends on the ratio of the refractive indices, to be precise it's arctan(n2/n1) radian - n2 is the refractive index of the medium the ray is passing into, water in our case, and n1 the refractive index of air). If the incident ray is at another angle, the resulting rays will be only partially polarized.

Nice application of the former: sunglasses.
Good sunglasses are polarized, ie they let only one direction of polarization pass (that's because they are made in such a way that the molecules in the glass (or rather in a special coating on the glass) can only oscillate in one direction). Now if we are smart and choose the right direction (vertical) most of the reflexes on the water will be gone (because their light was horizontally polarized).

printable version
chaos

Why oil on water looks like a rainbow	Why God doesn't ride photons	Mirth & Girth	Quant
Iridescent display	Polarization	wave-particle	Oscar
physics	radian	polarized light	photon
coordinate system	dipole	haggis	Polarizer
arithmetic

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