How Do They Form?
Fogbows are made the same way as rainbows, but with fog instead of rain. Rather than larger raindrops in the air, fog or low clouds are made of smaller water droplets. Why does this matter? Fogbows are colorless because they are formed by extremely tiny water droplets in fog, which causes sunlight to be diffracted rather than fully refracted and dispersed like in a rainbow. Another interesting fact is that fogbows are roughly the same size as rainbows. The next time fog is lifting, look in the opposite direction of the sun and you might just see one!
If you notice, there is a bright arc within the fog that takes the shape of a rainbow. All clouds, including fog (clouds on the ground), are made up of water droplets. When the sun shines into these water droplets, the light is refracted like a prism as it moves through the water separating the colors of the near white light to the full spectrum of colors. This creates the colors, but doesn't really explain the actual bow. As the sunlight moves into the water droplet, some of the light bounces off the back of the droplet and back toward the person viewing it. This bouncing is what creates a single bow, but if the light bounces a second time off the back of the droplet before coming back to the person viewing it, then you get a double rainbow.
