Nearly everyone has seen a rainbow, but is there such a thing as a snow bow or a fog bow?

That triumphal arch that fills the sky as wondrous storms depart,
I ask not proud philosophy to teach us what thou art. (Unknown)

Nice sentiments, but the secret has been out for some time now. Rene Descartes unlocked the mystery of rainbows in the early 1600s. His experiments showed that sunlight entering a spherical water drop is refracted, then reflected, before emerging in a direction opposite that of the Sun (antisolar point). Keep in mind that when the Sun is above the horizon, the antisolar point must always be below the horizon. To see a rainbow, the idea is to look toward a direction that's 42 degrees away from the antisolar point. Why 42 degrees? Think of a number of different rays of sunlight striking the face of one side of a drop of water. A ray that strikes the middle of the drop will bounce directly backwards, following the path it took coming in; however, rays entering from off-center directions will be refracted toward the center of the back of the drop and bounce off in a direction different from which they entered. It turns out that those rays that hit near the top edge of the drop are returned in a similar direction as the rays that strike elsewhere along the upper portion of the drop. The end result is that more rays emerge at an angle of about 42 degrees off from the direction which they approached the drop than for any other degree interval. Thus, the concentration of rays near this maximum angle of 42 degrees is responsible for the rainbow phenomenon.

Fortunately, we don't need to have a protractor with us to know if we're able to observe a rainbow. Basically, all we really need to do is look away from the Sun when it's raining. That doesn't guarantee a rainbow will be seen, but it certainly increases your chances of seeing one. We can see rainbows anytime of year, but the Sun must be no more than 42 degrees above the horizon. If the Sun is high in the sky (as it is near noon, for example), then the returned sunlight is no longer directed towards the surface. This is why we can see rainbows following an evening or morning shower, but not after a summer storm passes in the early afternoon.

Since snow is composed of hexagonal crystals and not spherical drops, the physics of light scattering is considerably different in falling snow than it is in the case of falling rain drops. Consequently, bows of light, opposite the Sun, won't be seen when snow is falling. Light entering hexagonal ice crystals results in halo phenomena. With halos, light is usually directed more toward the direction of the Sun rather than opposite it. While halos around the Sun may appear washed out compared to the vivid colors frequently seen with rainbows, the colors of some halo phenomena are every bit as vibrant as those found in rainbows. Halos, though generally not as eye-catching, have one big advantage over rainbows; they can be seen much more often.

Even though rainbows don't occur when snow is falling, it's indeed possible to see a rainbow over snow-covered ground. This can occur on rare occasions when rain is falling over snow-covered terrain and the Sun is unobscured by clouds. Another special case when a snow bow has been observed is when spray from Niagara Falls, for instance, is blown away from the Falls on a sunny day and remains briefly liquid before freezing. Robert Greenler has a photograph of such an occurrence on the jacket of his book Rainbows, Halos and Glories.

How about fog bows? Yes, fog bows, also known as fog dogs, cloud bows or white rainbows, can be observed on occasion. But even when one has formed, it may go unnoticed, since fog dogs are generally bereft of color. Whereas rain drops may be 0.5 mm in diameter, fog droplets are typically less than 1/10 this diameter. If you happen to see such a bow, you may notice that it's broader than a rainbow (rainbows cover about 2 degrees of the sky or about 4 times the width of the Sun or Moon), and there may be an orange tint on the outer portion of the bow. Actually, fog bows are caused by a diffraction of light rather than refraction and reflection. Because the fog droplets are so tiny, the wavelengths of visible light, which are obvious in the larger drops producing the rainbow, interfere with each other. The result is color bands that overlap. As the droplets get smaller, the interference is even greater, and the light that emerges is completely colorless. As with rainbows, in order to see a fog bow, you need to look in the opposite direction of the Sun.

By the way, shining you car's fog lights into the fog might possibly create a miniature fog bow, but you would have to be looking in your rear-view mirror to see it -- not a great idea under the best weather conditions. Actually, the jury is still out on the effectiveness of fog lights. You've probably noticed that if you try to use your high beams in fog, your visibility is greatly diminished, since the fog droplets scatter and reflect much of the light backwards towards your eyes. With low beams, there's less light scattered back to your eyes, so it's easier to see in foggy conditions.

According to Car Talk's Click and Clack (Tom and Ray Magliozzi), fog lights are mounted low on the front grill to illuminate the road surface beneath the fog. The yellow color of the fog lights likely makes little difference in terms of how penetrable these lights are in fog. However, contrary to what Tom and Ray state, the reason why fog droplets seem to reflect all colors of light isn't because they're so big. As mentioned above, they're tiny compared to rain drops. With these smaller droplets, the light that's scattered is concentrated more in a backward direction than is the case with larger drops. Anyway, it's nice to know that even if the ground is enshrouded in fog, it's still possible to see interesting atmospheric effects, like the rainbow's less conspicuous cousin.

For more about this question see Color and Light in Nature, by David Lynch and William Livingston, Rainbows, Halos and Glories, by Robert Greenler and The Rainbow Bridge: Rainbows in Art, Myth, and Science, by Lee and Fraser.

Also see the Earth Science Picture of the Day for today 2/14/03 (rainbow) and for yesterday 2/13/03 (lunar halo) http://epod.usra.edu/

Thanks to David Lynch of Aerospace Corp. and to Rebecca Kidd for their help with this question.

Dr. James Foster originated this series and did it as a solo project for the GSFC website for SEVEN YEARS! This year Dr. Foster has decided to share the enthusiasm he has for this project with other Goddard scientists and will be posing questions on a semi-regular basis.