Maria Jackson, of Dunedin, asks :-
A newspaper featured a photograph of a rainbow. I have what looks like the exact same photo, which I took on the same afternoon but 200 kms to the East. Can this be the same rainbow? If so how far can they been seen.
John Campbell, a physicist at the University of Canterbury who has an interest in light and colour in the atmosphere, responded.
Sort of, but different raindrops.
A rainbow is the coloured bow we see whenever raindrops are illuminated by the Sun behind us. When a ray of white light from the Sun enters a spherical droplet of water it travels through the droplet, reflects off the rear surface and re-emerges from the front surface. If we look away from the Sun we see a circular bright bow that appears to be at the same angle across as that formed by about four hand spans at arm's length. It is bright inside the bow and darker outside because light from greater angles doesn't get deviated backwards.
The colour display of the bow comes about because in water blue light travels slower than red light so a blue ray is bent through a larger angle than the red ray. Hence the outside of the bow appears iridescent red with the other colours predominating in turn through to violet on the inside of the bow.
It is a bow because there is the same angle between the ray from any of the water droplets and the line from the Sun through our eye.
The light from the Sun has come to our eye by being reflected from the inside of a drop of water hence it appears to come from the direction of the raindrops which are usually some way away. Hence the bows would look very similar, the main difference would be in the background, hills or cloud.
Apart from the background, there could be two differences. A photographer at a higher altitude than the other would see a greater arc of the bow. Also because the photographs were taken 200 km apart it means that the photographers were looking at a different set of rain drops. If the raindrops near the two locations were of different size, then for small raindrops there appears just inside the arc a fine series of colours and bands. Their appearance allows the size of small drops to be measured.