Fogbows and Drop Size

Important update: These pages have moved to their own domain at https://rainbowspec.observer, where their information, organization, and graphics have been significantly improved! This page is replaced by my new fog page.

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

Like with supernumerary rainbows, fogbows are a result of the wave nature of light, which is noticeable when the the droplets are smaller than 1mm in diameter. In fact, the wave nature of light is the whole reason rainbows look different when made by different drop sizes! Rainbow Drop Size I recommend reading the supernumerary page to understand this one, as understanding it relies on information provided in the supernumary page. Particularly about interference.

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. — The difference between light reflected from a 0.4mm and a 0.8mm drop, diagram made by Les Cowley at Atmospheric Optics

Another diagram from AtOpt, showing how the primary and supernumerary bands change in appearance and drop size decreases, units in microns (1/1000 of a millimeter).

As the droplets decrease in size, the length that the light must travel is shortened, thus there is not as much length for the wavelengths to get out of step with each other, thus the bands of light are wider and overlap more. If they are small enough the rainbow will be so broad that the colors overlap signifigantly, causing it to appear almost fully white. Rainbow Drop Size