The Science of Double Rainbows (OMG, what does this mean?)

This question came in from @holabendez for Science Week. What causes a double rainbow? The question is inspired by, in my opinion, the best youtube video since Keyboard Cat met Hall and Oates. Check out the Double Rainbow video below - if I'm this happy for just one day in my life, it will have been a happy life:



And now you'd better check out the Double Rainbow Song....



Rainbows are the result of the reflection and refraction of light by water droplets. They can be seen when there are water droplets in the air in front of you and sunlight shining from behind you at a low angle. You can also see them when looking at a sprinkler or hose, and sometimes they are created by the moon. But before we jump into the optics involved, let's review some high school physics.

White light and refraction:
White light from the Sun is made up of all the various colours of visible light. Each of these colours has a different wavelength - red light (at one edge of the rainbow) has a wavelength of ~650 nm, whilst violet light (at the other edge) has a wavelength of ~400 nm.

When light travels from one medium (say air) to another (water), it changes speed, and if the light enters at an angle, it will bend. This is known as refraction. Shorter wavelength light (such as violet) refracts more than longer wavelength light (such as red). You can see white light splitting into its constituent colours in the image to the right.

NB: The Sun may not look white from here on Earth (it looks yellow), but if you were to observe it from space, it would look white. This is because the Earth's atmosphere scatters shorter wavelength light (like violet) more than longer wavelength light (red). See our story on the dust storm that turned Sydney red for more discussion of atmospheric scattering.

Primary Rainbow:
Rainbows result from a combination of reflection and refraction. The pictures below show the optics of how this works. The grey circles are water droplets. White light enters the droplet and is refracted, then reflected off the back of the droplet, before leaving the drop split into its constituent colours, again refracted. Some light will travel through the droplet - the reflection is not 100%. Red light leaves the droplet at a slightly higher angle than violet - this angle is independent of the size of the drop, but does depend on its refractive index. Seawater has a higher refractive index than rain water, so the radius of a rainbow in sea spray is smaller than a rainbow in the sky. The following picture shows the paths of red and violet light in the production of a rainbow - the other colours of a rainbow (for example green) travel somewhere between the two extremes.



When you see a rainbow, you are seeing light that has been refracted and reflected through water droplets, however the red colour does not come from exactly the same droplets of water as the violet colour. If you were able to isolate one particular water drop that produced some of the red colour you saw, the violet light from this drop would not meet your eyes - it would travel over your head. The following picture shows that multiple water droplets contribute to the colours you see - this is why red is the top colour in the rainbow.



Secondary Rainbow:
In the immortal words of the above youtube video, a double rainbow, Oh My God, what does this mean? It means interesting optics. A secondary rainbow is produced when there is one extra reflection of light within the water drop. As some light is lost each time it hits the edge of the drop, the secondary rainbow is fainter than the first. It appears higher in the sky because the light exits the drop at a larger angle (50-53 degrees) than the primary rainbow (40-42 degrees).



The colours in the secondary rainbow are in reversed order to the primary rainbow.



The following picture shows how the rainbow appears in the sky with regards to the Sun and the observer. The same picture also makes sense for the secondary rainbow, however it would appear at a larger angle, and therefore could also appear later in the day when the Sun is higher in the sky - it would also have the colours reversed. If the Sun is higher than 42° (or 53° for the secondary), the rainbow is below the horizon and usually cannot be seen.



The reason that the rainbow is circular is that this is the only shape that reflects the light back to your eyes at 42° (or 53°) - water droplets below and above (or to the left and right) of the rainbow do not reflect the light to your eyes. What this means is that everyone sees a different rainbow. If you are looking at a rainbow and walk to a new position, the light you see in the new spot will have been reflected by different water droplets to the light you saw in the first spot. This is also why there is no pot of gold at the end of the rainbow - there is actually no end of the rainbow. A rainbow does not actually exist at a particular location in the sky - it all depends on your location and the position of the Sun.

It is possible to see a completely circular rainbow, but only if you are in a plane above the ground. In this case, you could look down and possibly see a rainbow whose centre is the shadow the plane. Climbing a mountain may not help you see a more complete rainbow as the mountain itself would cast a shadow, blocking the light which would cause the rainbow.

So even though a "double rainbow all the way across the sky" may seem a mystical experience, it's really just physics!

References:
G., T. (1938). Descartes' Discourse on Method Nature, 141 (3574), 769-769 DOI: 10.1038/141769c0

Ep 109: Tongan blowholes and whales

The Kingdom of Tonga is an archipelago in the South Pacific Ocean comprising 169 islands stretching over a distance of about 800 kilometres. It is the only sovereign monarchy in the Pacific and takes pride in its claim that it was never colonised.

I recently spent a wonderful two weeks in Tonga - the islands completely live up to their billing as the Friendly Islands - Captain Cook gave Tonga this moniker after his first visit in 1773 when he was treated to various festivals. It was only later that it was revealed local chiefs wanted to kill Cook but could not agree whether to attack by day or night.

This is the first in a series of podcasts about Tonga that include my own recordings from Tonga and also interviews with experts in the scientific areas we tackle. In this show, we look at:

1. The Mapu a Vaea blowholes - these blowholes are created by the ocean pounding into the coastal rock and moving through natural tunnels creating a fountain;
2. Tongan singing - not much science here, but it's beautiful!
3. Whale behaviour and migration - I chat to Scott Portelli, an award winning photographer and diver who runs whale-watching tours in Tonga. Scott recently won the prestigious Scuba Diver AustralAsia - Through the Lens Underwater Photography Competition with an outstanding photo from Tonga - see more of Scott's photos on his webpage. Scott runs Swimming with Gentle Giants, a company which conducts whale diving tours each year between August and October off the islands of Vava'u in northern Tonga. I chat to Scott about:
• his experiences swimming with whales,
• when to swim with whales,
• whale behaviour and migration patterns,
  
• the oceanic animals of Tonga,
  
• a little bit of whaling politics,
• the threats to whales, including whaling, global warming and pollution, and
  
• the fact that I once ate whale...

There are very few places left so get booking if you would like to swim with whales this year.

Stay tuned for more on Tonga in upcoming podcasts, in which we will talk about, and experience, the intoxicating drink Kava, the Stone-Henge of the South Pacific, the effects of global warming and rising sea-levels on Tonga, the local animals and more on whaling science and politics.

Listen to this podcast here:

And see below for some very cool traditional dance (also here if you can't see the video):

Volcanoes

What are volcanoes? What causes them, and where can we find them? Some of the biggest volcanoes on Earth are under the ocean. Are the connected to Earth quakes and tectonic plates?

Listen to the mp3 here