Rainbows, fogbows, and colours of sunlight
D. Indumathi, The Institute of Mathematical Sciences, Chennai

It is monsoon time, and the clouds and rains are making for a spectacular display. Not just their colours and shadows, but it is also rainbow time.
Rainbows are formed when sunlight is reflected from falling raindrops.  We know that sunlight looks white because it has all colours in it, from indigo and deep blue to green, yellow, orange and red. The reason rainbows are coloured is that the speed of different colours in water is slightly different. When sunlight enters a raindrop, it is crossing an air-water interface and gets refracted. The different colours get refracted by different amounts; see colour picture on cover.
Now, if the angle of the Sun is just right, an interesting thing happens. The light rays, going through the rain-drop, encounter the back end of the drop. This is a water-air interface. There is a special property of light when it goes from a denser to a rarer medium (water to air, with refractive index n1=1.33 and n2=1.00 respectively). If the angle of incidence q is such that sin q>n2/n1 (about 48 degrees for water-air interface), then the light is not refracted but gets totally internally reflected back into the water-drop. After this reflection, it hits another interface, gets refracted, and exits the waterdrop, and reaches our eyes. 
It can be calculated (you can try it, just using the laws of refraction; see figure) that the light from the Sun bends by about 40-42 degrees (blue-red). These rays look like they are coming from a circular arc in the sky and form the rainbow. In fact, if you are viewing from high up, you can see the entire circular rainbow.
When the light makes one more internal reflection before exiting the raindrop, it makes a secondary rainbow and is at around 51 degrees in the sky. It is higher and fainter (because of the extra reflection) than the primary rainbow, and also has the colours reversed; see cover of JM.  Also remember that the sunlight causes rainbows, so the rainbow is always seen opposite to the Sun.

Fogbows
You can see "white" rainbows too. This happens when there is thick fog in the air. Fog contains water droplets that scatter the light. But these are much smaller (1/10 mm as opposed to 2-3 mm for raindrops).  Hence the colours do not separate clearly and fogbows are mostly white with sometimes a hint of colour.

Moonbows and other bows
When the moon is full or nearly full, it can be bright enough to form a "moonbow". Even spray from a waterfall is sufficient to make rainbows curving through the air with light from the moon!
Don't forget to look out for all these rainbows this season. Happy hunting!