# BrewsterAngle

Zero loss? Shine light on a clear piece of glass at just the right angle and none of it reflects? It can happen ...

Light is polarized. Electromagnetic waves vibrate: some up/down, some left/right. When light encounters a transparent medium, like a window or the surface of a lake, part of the light bounces off and part goes through, following a bent path. Both polarizations take the same route.

But the two polarizations don't need to act alike as far as how much light gets reflected and how much gets transmitted --- and they don't. One polarization (the one that's left-right relative to the surface) reflects increasingly well as the light meets the medium at a flatter and flatter angle, until at a grazing incidence it almost all bounces away, like a stone skipping off a pond. The other polarization acts similarly at extreme angles (0 and 90 degrees) but in between its fractional reflectivity takes a strange dip.

There's a magic angle --- called Brewster's Angle --- where the dipping reflectivity curve touches zero. No light of the up/down polarization reflects from a surface at that angle. (For water or glass that angle is ~55 degrees away from the vertical.) If you want to make a window that's perfectly transparent (to one polarization, anyway), slant it at the Brewster Angle. Some lasers have a kind of a skewed end for precisely that reason: maximum efficiency. And if you want to cut glare, the way "polaroid" sunglasses do, align the polarizers to block out the type of light that mostly reflects toward you.

But why does light behave like this? One way to understand it is to tunnel down to the atomic level and think about the details of reflection there. Look closely at the front surface of a pane of glass. Light doesn't "bounce" like a rubber ball. In reality, the light (or rather, its electric field) shakes billions of tiny charged particles, electrons, inside the glass. Shake a charge and it must radiate: those electrons in turn produce new electromagnetic waves. The freshly-minted waves interfere with each other, in exquisite harmony, to make "reflected" and "transmitted" rays of light that we're used to seeing on a larger scale.

But a shaken charge doesn't radiate equally in all directions. Just like a radio antenna which can't pick up signals from certain orientations, an accelerated charge can't give off any electromagnetic waves along its motion. One of the two polarizations of light shakes the electrons in the glass so that, at the Brewster Angle, those shaken electrons simply cannot emit any energy in the outward, reflected direction. They've got no choice --- they simply must pour all of their energy into the transmitted wave.

And thus, a perfect window ...

(The same sort of microscopic explanation works at the quantum level, where wavefunctions of photons and electrons interact with varying probabilities. See also FringeOfThings (25 Jun 1999), CoherentInterference (28 Dec 1999), ... )

TopicScience - 2004-02-19

(correlates: FreeTrope, FringeOfThings, Zhurnal Three, ...)