A rainbow occurs when rain is falling in one portion of the sky and the sun is shining in another. For a rainbow to be seen, the sun must be behind an observer who is facing falling rain.

If the angle between the refracted light and the normal to the drop surface is greater than a critical angle, the light reflects off the back of the drop.

The critical angle for water (which would apply to raindrops) is 48 degrees (relative to the normal). Therefore, if light strikes the back of a raindrop at an angle greater than 48 degrees, it will be reflected back. If the angle is smaller than 48 degrees, the light will simply pass on through.

The reflected light is refracted as it exits the drop. Violet light (bending the most) emerges at an angle of 40 degrees relative to the incoming sunlight while red light (bending the least) exits the drop at an angle of 42 degrees. Other colors of the rainbow leave a raindrop at angles somewhere in between. According to Descartes' calculations using laws of optics, the three stage refraction-reflection-refraction pattern that light undergoes when passing through a raindrop produces a concentration of outgoing rays along a line that is 42 degrees above the head of an observer's shadow. This concentration of light rays is the rainbow that we see.

Since only one color of light is observed from each raindrop, an incredible number of raindrops is required to produce the magnificent spectrum of colors that are characteristic of a rainbow.

water droplets

Terms for using data resources. CD-ROM available. Credits and Acknowledgments for WW2010. Department of Atmospheric Sciences (DAS) at the University of Illinois at Urbana-Champaign.

primary rainbow