Rainbows

Rainbows result from refraction of sunlight in falling water droplets plus reflection of the light from the back of the droplet.

If during a rain shower you can see the shadow of your own head, then you are in position to see a rainbow if conditions are favorable. The rainbow forms a circular arc around the anti-solar point, which is located at the shadow of your head. You can search for the shadow of your head to find a rainbow in a waterfall, or even in the spray from a hose or sprinkler. (Photo by Dubby Waggoner, used by permission.)

Primary rainbow Secondary rainbow Supernumerary arcs Rainbow image

Primary Rainbow

The primary rainbow forms between about 40° and 42° from the antisolar point. The light path involves refraction and a single reflection inside the water droplet. If the drops are large, 1 millimeter or more in diameter, red, green, and violet are bright but there is little blue. Such large droplets are suggested by the rainbow at right. As the droplets get smaller, red weakens. In fine mist, all colors except violet may disappear. Even finer fog droplets, smaller than 0.05 mm, produce the white rainbow or fog bow. The secondary rainbow involves two reflections inside the falling droplets.

Photo by Dubby Waggoner, used by permission.

Rainbows are not seen in midday since the whole 42° circle is below the horizon at most latitudes. So rainbows tend to be seen most in the later afternoon when a thundershower has passed and the sun from the west is illuminating the receding edge of an eastwardly moving raincloud. It is possible to see the entire circle of the rainbow from an airplane since there can be falling droplets both above and below you.

Secondary Rainbow

The secondary rainbow is about 10° further out from the antisolar point than the primary bow, is about twice as wide, and has its colors reversed.

According to Schaaf, the light of the secondary bow is one-tenth the intensity of that of the primary bow, given the same viewing conditions.

Photos by Dubby Waggoner, used by permission. Note the reversal in the order of the colors in the secondary rainbow. These photos also show the increase in brightness inside the primary rainbow. The region between the two rainbows should be a bit darker than the sky just outside the secondary rainbow, but this is a smaller difference.

Higher Order Bows

The third order bow has an arc of 40°20' around the sun itself, so you would have ot look back toward the sun to see it. Schaaf reports that it has been seen a number of times in nature, but that no record of the sighting of the fourth order bow is found. A sighting of the fifth order bow is attributed to nineteenth-century scientist Eleuthere Mascart. It would be positioned between the primary and secondary rainbows and would be about 7° wide, its red overlapping that of the primary bow. Rainbow orders up to thirteen have been seen with a laser and water droplets in the laboratory. Experiments for the observation of higher order bows are described by Jearl Walker in "The Amateur Scientist" section of the July 1977 issue of Scientific American.