Last Fall 2010/Winter 2011, I taught the science of weather and climate to non-scientists at Toronto’s York University.
During the Fall semester, a unit of NATS 1780 focused on atmospheric optics. Not surprisingly, rainbows were one of the topics that received attention.
By the end of this unit, students understood that rainbows are the consequence of a twofold optical manipulation of sunlight:
- Raindrops bend sunlight. Not only do raindrops bend (refract) sunlight, they do so with extreme prejudice. Blue light gets bent the most, red the least. In other words, this is a wavelength-based prejudice: The shorter the wavelength, the more the light is bent. This highly selective refraction is known as dispersion. Like a prism then, raindrops allow for the individual colours that comprise visible light to be made evident.
- Raindrops reflect sunlight. Inside the raindrop, reflection occurs. In fact, multiple reflections can occur. And if all of the angles are just right, these reflections can remain contained within the raindrop. This is known as the phenomenon of Total Internal Reflection (TIR).
The combined effect of bending and internally reflecting is best understood with a diagram. Note in this Wikipedia diagram that sunlight interacts with the air/raindrop boundary upon entry, gets reflected internally once, and then again interacts with the raindrop/air boundary upon exit from the raindrop. Taken together, the result is a single rainbow.
How are double rainbows produced? By increasing the number of internal reflections to two.
Single and double rainbows are relatively easily observed.
On the Fall 2010 Exam in NATS 1780, I included the question:
If it were possible, how would a tertiary (i.e., third)rainbow be produced?
A number of students correctly answered that three reflections internal to the raindrop would be required to produce such a phenomenon.
Although I had intended this to be a question of theoretical merit only, I was delighted to learn that both triple and quadruple rainbows have been observed – in other words, they are no longer just a theoretical possibility. (Quadruple rainbows would require four internal reflections.)
Alas, I’ve only ever been able to capture single and double rainbows … My personal quest for the more elusive triple and quadruple rainbows continues …
Ian Lumb's Blog 
Ian for a good accessible discussion of this topic and others I recommend
“Rainbows, halos, and glories By Robert Greenler”
Thanks for the pointer, Jim! -Ian
“Computer Simulations Shed Light on the Physics of Rainbows”,
http://www.scientificcomputing.com/news-DA-Computer-Simulations-Shed-Light-on-the-Physics-of-Rainbows-121411.aspx.