A rainbow is “an arch of colors formed in the sky in certain circumstances, caused by the refraction and dispersion of the sun's light by rain or other water droplets in the atmosphere” according to dictionary.com.
There are many different kinds of rainbows that can be seen. These are: Primary Rainbows, Secondary Rainbows, Spurious or Supernumerary bows, Fogbows or white rainbows, lunar rainbow and others.
A primary rainbow is usually the brightest rainbow. The arc of this bow has the color red on the upper part of the arc, violet is on the inner one. A primary rainbow occurs when light is refracted when it enters a rain droplet. It is then reflected on the inside back and then refracted again on the way out of the droplet.
In a secondary rainbow the light is reflected twice inside the water droplet. This causes the colors of the rainbow to be in reverse order as those in the primary rainbow. They are also located nest to the primary rainbow. A tertiary or quaternary rainbow can also occur by have the sunlight reflect inside the droplet three or four times.
Supernumerary, or spurious, or stacker, rainbow occur infrequently and occur on the inner side of a primary rainbow. Even more infrequently they may occur on the outside of a secondary rainbow. The color bands are pastel in color and do not fit in the usual color pattern.
Fogbows occur when there is fog, not rain. They are also known as white bows because that is the color that is most noticed. The color is due to the small water droplets. Fogbows can have secondary or even tertiary arcs also.
Lunar Rainbows form around the moon when it emits white light which is then refracted and reflected by a raindrop into the atmosphere. Since moonlight is not very bright, this type of rainbow is seldom seen.
Depending on the atmosphere or availability of certain surfaces other rainbows are known to occur. A red rainbow only happens at sunset. In this type, the light needs to travel far to reach the water drops. Due to the distance the blue end of the spectrum does not occur or it is scattered. Spider web rainbows are those rainbows that form from dew covered webs. These show only fragments of a rainbow.
When the spray from tires is the source of the water drops, a road spray bow is the effect. Geyser bows occur when a spray from a geyser is going off. Then mist bows are the rainbows that are seen from a watering hose.