Death Valley National Park, California
I checked with Wikipedia to see what the “official” name of this phenomenon is and was surprised to find out that it is called a 22° halo, so named because they usually have “an apparent radius of approximately 22° around the Sun or Moon.” That seemed really strange to me because I don’t think I’ve ever seen radii expressed in terms of degrees before, and at first I couldn’t figure out what angle they were talking about. Never fear though, Wikipedia goes on to give a detailed explanation including an easily understood application of Snell’s law:
- θ deviation = θ incidence + sin − 1 [ n sin ( π 3 − sin − 1 sin θ incidence n ) ] − π 3 .
Hah, just kidding, I don’t understand it either. To add insult to injury the Wikipedia article then goes on to explain how to “intuitively” understand what all the calculations mean. All I was able to glean from that further explanation was that the author (most likely a physicist of some ilk) doesn’t really understand what intuitive means.
But one small illustration in the article did confirm that my own “intuitive” idea of the what the angle in question is. Imagine a stick pointing from your eye to the sun (don’t use a real stick for obvious reasons). Then imagine a second stick pointing from your eye to the halo ring. Grab that protractor (plastic, or metal if you’re really old) you’ve been saving since your school days and measure that angle and it should come out to be about 22°. The proof, as they often say in the math world, is left to the reader, or Wikipedia.