Is the light from the rainbow polarized? Very much so. How and why? And what about the wonderful halos? And the mysterious glory crowning the Specter of the Brocken?  And the beautiful aurora? Coronas? Zodiacal lights?

Rainbows are the most famous of many extraordinary displays that can be seen in the sky. Everybody seems to love them, from children to old men, and few wouldn't stop at least a few seconds to admire a fully developed rainbow. It has to do, undoubtedly, with its beautiful sequence of colors; but also with its perfect geometrical shape against the random background of clouds. If one could see the polarization of the rainbow a new order would become apparent: the rainbow is strongly polarized. Indeed, with a polarizer its contrast significantly improves and you can find otherwise undetectable rainbows!

Rainbows form the arc of a perfect circle centered on the shadow of your head. Yes, that's right. Everybody sees a slightly different rainbow even if standing side by side: each one has his own personal rainbow! If you are not sure where a rainbow should appear during rainy weather do the following. Look for the shadow of your head on the ground; that's the center of the circle (antisolar point). Next, find the radius by stretching in a line your two hands (thumb to thumb) at arm length. Of course, if the tip of your finger doesn't reach above the horizon, then the sun is too high for a rainbow.

The drops of water refract and reflect the rays from the sun backwards, at 42 degrees to the incoming rays. Thus, the rainbow is seen in a direction opposite to the sun as a circle of that radius, an angular size which is independent of your distance to the raindrops. This is also true for the rainbow produced by a watering hose: no matter how much you step back, you won't be able to include its full diameter in your photograph (you need a very-wide-angle lens for that). Of course, when you step back, the individual drops forming the arch will change. The largest rainbow (half a circle) appears when the sun is close to the horizon.  However, from airplanes, mountains or tall towers, where one can see raindrops below the horizon, the rainbow can be as large as a full circle.

Two refractions (A,B) and one internal reflection (C) inside the spherical water drops form the primary rainbow. A secondary rainbow, which sometimes appears outside the primary one (at 51 degrees) is caused by two internal reflections instead of just one. An interesting side note: small raindrops remain almost perfectly spherical falling through the air; very large raindrops are deformed but, contrary to popular belief, they are flattened vertically instead of becoming elongated and pear-shaped as the archetypal cartoonish drop.

The color sequence of the rainbow is caused by the two refractions (A,B) as red is refracted slightly less than blue. On the other hand, the polarization of the rainbow is caused by the internal reflection (C). The rays strike the back surface of the drop close to the Brewster angle, so almost all the light reflected is polarized perpendicular to the incidence plane (perpendicular to the monitor screen). This is similar to the way the glare of the sun on the sea is polarized, except that now the reflecting surface is not horizontal. As the incidence plane is determined for each drop by the plane containing the sun, the drop, and the observer, the rainbow is polarized tangential to the arch. Thus, a vertical polarizing filter will produce a gap at the top of the rainbow while enhancing the contrast of the sides.

The primary rainbow is 96% polarized while the secondary is 90% polarized. The extra brightness of the sky inside the primary rainbow (and outside the secondary rainbow) is also polarized tangentially (but to a lesser degree) as it has the same origin as the bows. With a filter pointing radially it disappears together with the rainbows and becomes undistinguishable from the dark Alexander's band between the bows (named after Alexander of Aphrodisius, AD 200).

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