As the name might suggest, a fogbow is the name given to a phenomenon created by the same process of refraction and reflection that creates rainbows, but formed instead by the water droplets in fog, mist or cloud, rather than raindrops.
What is a fogbow?
A fogbow is similar in some respects to a traditional rainbow. It forms from sunlight interacting with water droplets contained in fog, mist or cloud rather than interacting with raindrops as it does in a classical rainbow. These water droplets are much smaller than raindrops, nearly always less than 0.1mm in diameter.
These tiny droplets cause the light to undergo different physical processes, most notably diffraction, which leads to fogbows appearing to be devoid of colour. It is for this reason that fogbows are sometimes known as white rainbows.
Fogbows are often seen alongside another optical phenomenon, also caused by diffraction, called a 'glory'. A glory is a sequence of multiple, pale-coloured rings at the bows centre - as can be seen in the image below.
How fogbows are formed
The elements that make up a fogbow are the same as for a rainbow - sunlight at the observers back, and water droplets in front. The water droplets that make up fog are so tiny compared to raindrops, between 10 and 1000 times smaller, that while the light still reflects from the water droplet back towards the observer, the process of diffraction of the light by the droplet becomes a dominant effect.
The process of diffraction broadens the reflected beam of light which smears out the colours which give the characteristic ghostly white, or very faintly coloured fogbow. This also makes the fogbow much broader than a rainbow.
The fog bank has to be relatively diffused and thin to allow the light to pass through the droplets and create the effect. Fogbows are large, almost as big as rainbows
A similar effect can also be seen from aircraft in cloud droplets, when they're known as cloud bows.