Fogbows and Drop Size

soft white arc in a foggy sky above trees Peter Lowenstein - EarthSky.org

Fogbows (and cloudbows) are formed similarly to rainbows, but since the water droplets in clouds and fog are much smaller than the raindrops in rainbows, the appearance of the bow is different. Note that fogbows and cloudbows are the same phenomenon, since fog is just clouds low to the ground.

The bigger the raindrops, the thinner the rainbow. Likewise, the smaller the drops, the wider the rainbow. Cloud and fogbows feature waterdrops from 1 micron to 100 microns, usually 10 to 20 microns. Bows made from larger droplets will not only be relatively narrower, but more colorful than bows made from smaller droplets (which will be wider and paler). Fogbow Droplet Size - AtOpt

diagram showing bands of light when passing through a 0.8mm drop versus a 0.4mm drop. The primary bow and supernumaries of the 0.4mm drop is wider than those of the 0.8mm drop. Rainbow Drop Size - AtOpt
diagram of rainbow and fogbow arcs at different raindrop sizes. At 800 microns the rainbow is thin and colorful. At only 12 microns the fogbow is very wide and white Fogbow Droplet Size - AtOpt

Both simulations show how the primary and supernumerary bands change in appearance according to drop size. Notice how as the drops get smaller, the width of the bands increase.

So why does the width of the bow increase? And why does the number of supernumerary bands decrease as the drop gets smaller (considering if the drop is too big, we cannot see them)?

It comes back to the same wave interference that causes supernumerary bands (read that page first).

two diagrams comparing the wave interference of light exiting a drop of water after reflecting once inside of it. One drop is bigger and has shallow curved wavefronts, and the other is smaller with curvier wavefronts. Like a Bridge Over Colored Water

Notice how the wavefronts overlap for each drop. For the water drops that are smaller, there is less distance within the drop for the overlapping waves to get out of step with each other. The overlapping waves from larger drops have more distance to be able to get out of step with the other waves. Thus the smaller drops have wider bands of dark and light, including the primary bow, which is at the very edge. The larger drops have thinner bands of dark and light. Hence why smaller drops make wider bows and fewer supernumeraries.

The primary band for each color broadly overlaps due to each being so wide, thus they combine to form a white bow rather than a rainbow.

There may be a glory at the center of the fogbow, since they are created by the same kind of conditions. This is rarely seen however, since the viewer must be at a high vantage point to see more than half of the rainbow.

Suggested next pages: Glories Corona and Cloud Iridescence