Jenny Harris, of Balclutha Primary School asks :-
I photographed a triple rainbow. Is it rare or just unusual for this to happen and what causes this?
John Campbell, a physicist at the University of Canterbury who has an interest in light and colour in the atmosphere, responded.
What a fantastic photograph. The main bow is always seen when sunlight falls on raindrops. The secondary bow less often and is best seen when the background is dark, e.g. sunlight doesn't fall on a forested hill. The coloured bands just inside the main bow isn't a rainbow and is rarer.
First consider the main bow. It is observable as that part of a circle where sunlight is incident on raindrops. The circle subtends an angle of about 42 degrees about the line passing from the Sun through your eye when looking away from the Sun.
Notice that it is lighter below (inside) the circle than it is above (outside the circle). When a ray of light enters the surface between two different materials, in this case going from air into a water droplet, it slows down on entering the more dense material, in this case to three quarters the speed it had in air. A change of speed at the surface means that some of the light is reflected back at the surface, in this case about 2% where the ray hits the surface perpendicularly. 98% of the intensity of the ray is transmitted into the droplet. 2% of that intensity is also reflected backwards to the eye from the far side of the droplet.
If the ray enters the droplet other than perpendicularly, because the speed changes the path of the ray is deviated, some is reflected off of the back surface, and deviates again on exiting the front of the drop, back to our eye at an angle other than that along the eye-Sun line. If we use the theory of electromagnetic waves (light) we can show that for all angles of incidence there is a minimum angle of deviation of the light, in this case about 360 minus 42 degrees, which explains why it is brighter inside the bow than outside.
The bow itself is a "minor" effect. In a dense material (eg water) red light travels slightly faster than blue light hence the minimum angle of deviation is greatest for red light. This explains why the outer edge of the bow is red, the only pure colour in the rainbow, and anywhere inside that the colour is predominately another (pure) colour mixed with a bit of red and the other colours that peak outside it.
Now consider the second bow (about 50 degrees). That is because now the ray has reflected twice inside the droplet before coming back to the eye. This has a maximum angle of deviation so it is brighter outside this bow than inside and the colours are reversed. It appears much weaker because of the two internal reflections needed.
The "third" bow in your photograph (the coloured bands just inside the primary bow) is a different effect. It is due to interference of the waves inside small droplets of rain. Its structure can tell you the size of the falling raindrops illuminated.