Rediscovering the rainbow

I’d seen enough rainbows. As a child they seemed rare enough that each one had to be exclaimed over. But I’d seen enough by now, I’d seen them all… or so I thought, but I thought wrong:

Rainbows over Adelaide in August 2012.

Rainbows over Adelaide in August 2012.

Once I’d recovered from the awe, I had some questions. How is this particular rainbow formed? And how do I even begin to describe it?

To answer those questions I first needed a refresher on how your garden variety rainbow is formed.

A rainbow is the result of sunlight (which is white light, composed of all the colours of the… well, rainbow) being refracted and reflected through a raindrop. Parallel rays of light hit the spherical raindrop and they refract (move through one medium – air, into another – water) through to the inside of the raindrop. At this point, the light can refract again and leave the raindrop in a similar direction to which it entered. If this is the case – no rainbow. Alternatively, the light can be reflected (bounced around) inside the raindrop before it is refracted. In this case, a rainbow can form.


Light refracting and reflecting through a raindrop.

Each of the colours of the rainbow has a different wavelength and so is refracted at a slightly different angle, splitting white light into the colours with which we are so familiar – red, orange, yellow, green, blue, indigo and violet (ROYGBIV). This principle of dispersion (the separation of white light into its constituent colours) is nicely demonstrated when shining light through a glass prism.


White light dispersed into its constituent colours: ROYGBIV

That is how the beautiful, yet common, primary rainbow is formed. In order to get secondary rainbows the light must be reflected twice before leaving the water droplet; three reflections give a tertiary rainbow and four reflections give a quaternary rainbow.

Have you ever noticed that the colours of secondary rainbows appear in the opposite order to the primary rainbows (VIBGYOR instead of ROYGBIV)? The second internal reflection, combined with the curve of the raindrop, causes this reversal of the colour order. A third reflection switches the rainbow back to ROYGBIV and so on and so forth. 

Since higher order rainbows are simply the product of more reflections inside a raindrop, it doesn’t seem too difficult to make tertiary and quaternary rainbows. But these rainbows are incredibly rare and there are a couple of reasons for this:

  1. With each reflection some light is lost to refraction and so the higher order rainbows become dimmer and dimmer and;
  2. At the same time, the angle at which the light is refracted out of the rainbow (relative to which it came in) is increasing – essentially, the light is turning back on itself and heading back in the general direction of the sun. It’s much more difficult to see the dim tertiary and quaternary rainbows when they have the bright sun as their background!

Reports of sightings of tertiary rainbows have appeared in texts since the 18th century, but the first photograph of a tertiary rainbow was not taken until 2011. Shortly after, a quaternary rainbow was also captured. Both were photographed in very specific conditions: dark background clouds with brightly lit rain between them and the observer. It’s also likely that raindrops with an oblate (flattened spherical) shape are more likely to produce higher order rainbows. Even with these conditions, the images had to be manipulated to reveal the tertiary and quaternary rainbows.

There are many more weird and wonderful rainbows you can see if you happen to be in the right place at the right time. Raindrops of uniform size are good for producing supernumerary rainbows: bows of decreasing radius that appear within the primary rainbow, each smaller bow fitting snugly within the larger one, although with some colours missing.

This phenomenon could only be explained once we understood the properties of light. While Isaac Newton could explain the refraction of light in the 18th century by thinking of light as a particle; it was only when Thomas Young established the wave theory of light in the 19th century, that the formation of the interference bows in supernumerary rainbows could finally be explained. (We now understand that light possesses both wave-like and particle-light properties.)

As we discussed earlier, light is reflected off the inside of the raindrops and the curved surface means that some light travels slightly further than others. When the light hits the other side, the peaks and troughs of the light waves that have travelled slightly different distances will either coincide or differ. The varying path lengths of the light will result in the light spreading out over a large distance and producing a wavefront.

At points of the wavefront where the peaks of the light waves coincide, light is amplified and these colours are visible in the supernumerary bows. Where the troughs of the light waves coincide, the wavefront has a very low intensity and these colours are not visible. A supernumerary rainbow is characterised by the absence of some light!


A supernumerary rainbow.

So there you have it, the ‘how’ of the formation of that stunning combination of primary, supernumerary and secondary rainbows that I saw recently. But that’s not where rainbows end: for more on rainbows – including other kinds like fog bows and halos check here. If you just want to see photos of a plethora of rainbows in all their glory, then you cannot go past this site, where rainbow hunters share their hunting trophies and give you every opportunity to reclaim a child-like awe of bows.

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