The Science of Rainbows

The science of rainbows can be easily explained as a combination of water droplets and light, that spreads out into an spectrum of colours. You will see a rainbow when the sun is behind you and there is moisture in the air in front of you - this is important to remember when understanding how they are formed.

The Refraction of Light
Light bends and changes direction when it travels from one substance (medium) to the next. Different mediums cause the light to travel at different speeds. To understand how a rainbow works, physicists use the example of a glass prism to explain light refraction through a raindrop. So when light hits the medium of a glass prism, it refracts (bends) and disperses through the prism. The same happens with a water droplet. The arc of the rainbow appears by the angle the sun hits the droplet, the bending of light through millions of water droplets causes the colours to be shown in a semi circle. This process is called "Snell's Law of the Refraction of Light." See the image below for a demonstration:

Light Dispersion. Source: Kalki at Wikimedia

White Light
We see light as white, but it is made up of many colours. When the beam of light passes through the water droplet it slows down and spreads out or disperses, separating each colour that makes up white light as a spectrum of colours. The colours we see in a rainbow are:

red, orange, yellow, green, blue, indigo and violet.

There are other colours, but we can't see them through our human eyes - even infra-red and ultra-violet! The index of refraction is the measure of speed of the wavelength of colour and each one has a different speed of refraction. You will see the colours of the rainbow in the same particular order because of this speed.

This image below shows light passing through a glass prism, which illustrates what happens when light passes through water droplets. You can see that the beam of strong white light hits the glass and reflects up (the thin white line) and it also refracts through the glass, dispersing out the other side in a spectrum of colours.

Summary : A rainbow is made up of millions of water droplets, each one refracting and dispersing sunlight. The sun is hitting every droplet at a low angle and is situated behind you as you look at the rainbow. The arc is caused by the way the light is bending through the droplets. And that, in a nutshell is the science of rainbows!

If you want to learn more, click here to read this excellent guide The Calculus of Rainbows

Prism by chris-dcx, on Flickr Creative Commons

Primary Rainbow. Source: Listentoreason at Flickr Commons

Primary rainbows shows red as the colour on the outside, leading through to violet on the inside. You will see a primary rainbow at an anti solar point of 42 degrees. An anti solar point is the shadow of your head, directly away from the sun. In the photo above you can see the primary rainbow very clearly.

Secondary rainbows occur when the water droplets in the primary rainbow reflect light twice. Because it is the reflection of the primary, the colours are reversed. The colours are not so clear in the secondary and it is generally fuzzier and flatter than the primary. This rainbow occurs at 51 degrees from your anti solar point. Take a look at the image below, this shows both primary and secondary rainbows clearly.

Primary and Secondary Rainbows. Source: D Sharon Pruitt at Flickr

Rene Descartes (1596 - 1650) was a famous philosopher who came up with the modern theory for how rainbows occur in 1637. He was the first person to make the relation between round water drops and the interaction of refracting light. This is his sketch for how primary and secondary rainbows are formed.

Rene Descartes' Rainbow Sketch. Source: Wikimedia

Alexander's Dark Band is the name for the dark sky between the primary and secondary rainbows. It was named by Alexander of Aphrodisias, a Greek Philosopher who first noticed these optical phenomena in 200AD.

Alexander wrote commentaries on Aristotle's works and it was in writing a commentary to Aristotle's "Meteorology" book that he mentioned the dark sky between rainbows.

Primary rainbows light up the sky inside of the arc, the secondary rainbow is a reflection of the primary so it brightens up the sky on the outside of the arc. This makes the sky appear darker between the bands.

Supernumerary Rainbow.
Source: Fir0002 at Wikimedia Commons

The Supernumerary Rainbow is a selection of smaller multiple green, pink and purple colours in the inside of the main rainbow. The extra bands are created by the interference of light waves on the water drops. The colours are lighter than those in the primary rainbow, and can change colour too.

You can sometimes see a supernumerary bow on the outside the secondary rainbow, but these bands are very faint.

A very good explanation of how these bands are formed can be found at www.atopics.co.uk

This amazing circular rainbow appears almost round because it was taken from an aeroplane! You can sometimes see these round arcs in mountains or a reflection in the water too. This is because the Earth's horizon is not in the way of showing the full circle!

Round rainbow by Hans (lumilux.org), on Flickr Creative Commons

Twin Rainbow.
Source: Tlatla at Wikimedia Commons

There's currently no agreed explanation for Twin rainbows!

Scientists believe that they may be caused by a mixute of ice crystals and water droplets. Another reason could be that twin bows appear because of non spherical water droplets, this makes the light refract slightly differently, resulting in a twin rainbow.

Another explanation is that the second bow is a reflection of the first, but this hasn't been concretely proved because there have been rainbows that have a reflection and a twin too!

Sunshine in the Mist Makes for....by cogdogblog, on Flickr creative commons

Rainbow in Sprinker Spray
Photo by Georges Noblet at Wikimedia

This photo was taken in a park in France and shows a rainbow of crepuscular rays in sprinkler spray. A crepuscular ray is light that appears from a single point in the sky, and look like columns of light. The columns of light here are from the trees above and as they shine onto the water droplets from the sprinkler they make a rainbow.

A fun experiment to do yourself or with a child is to make a rainbow with hose water! On a sunny day go outside and set up a hose to spray a fine mist, stand with your back to the sun and turn the water on. Remember that the anti solar point is the shadow of your head and that the angle for a rainbow is 42 degrees from this point. Move the hose slowly from the shadow of your head to what you perceive 42 degrees will be - you will then make a rainbow! The brightest rainbows are later in the day, so try this as late afternoon for the best results.

Red Rainbow at Sunset. Source: Jurvetson at Flickr

Red rainbows can be seen at sunset, the low sun lengthens the red and yellow wavelengths in light and scatters the shorter greens and blues.

Moon bow. Source: Thoth, God of Knowledge at Flickr

A moon bow is a very rare occurrence and you are lucky to see one! It is caused by the moon behind you, rather than the sun. It looks like something from a dream doesn't it?

Fogbow by Thoth, God of Knowledge, on Flickr

A Fog bow is formed the same way as a rainbow, but the water droplets are smaller in fog so you cannot see the colours. This ghostly arc is most commonly seen on mountains and in cold sea mists. This photo was taken on a hillside above San Francisco.

"Let no one who loves be unhappy, even love unreturned has its rainbow"
James M Barrie
(Scottish author and dramatist, 1860-1937)

This stunning image is a Circumhorizon Arc, but not a rainbow. It is created by a high sun, at about 58 degrees and is created by ice particles found in high level cirrus clouds. This optical phenomena is seen in mid latitude countries, so whilst it is very rare to see this in countries nearer to the Northern Hemisphere. Do you live in Los Angeles, Houston or Melbourne? If so then you can see this beautiful sight up to 6 times over the summer, if you live in Northern Europe then to see this would be very unusual indeed!

Circumhorizon Arc. Source: Sazzagre6 at Photobucket

The sky is smiling! This is a Circumzenithal Arc, which is also created by ice crystals and the sun. The ice crystals must be flat and six sided, the sun has to be angled at 32 degrees - with these conditions you can see why this is a rare occurrence! It is most commonly seen in colder climates and will often stay visible in the sky for up to 30 minutes.

Circumzenthial Arc by dev null on Flickr Creative Commons