Tubby Hopkins, of Dunedin, asks :-
What actually defines the arc of a rainbow? Is it the time of day, position of the sun, season? There appears to be many different degrees of curvature, some appear high with a small radius, others low and flat etc. Regardless, no matter how hard I look, I'm still chasing that "pot of gold"
John Campbell, a physicist at the University of Canterbury with an interest in light and colour in the atmosphere, responded.
A rainbow is the coloured bow we see whenever raindrops are illuminated by the sun behind us. They can be full circles if the conditions are right.
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 at a subtended angle of about 42 degrees. It appears to be at the same angle across as that formed by about four expanded hand spans at arm's length.
The colour display of the bow comes about because in water blue light travels slightly 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.
We normally see only part of the circular arc of the rainbow. The lower the sun the more of the arc we can see hence what we see depends on the time of day and year, our latitude, our altitude, and our surrounding geography. If we stood on a sharp mountain or an isolated high building we could see most of the circle if not all of it. From a plane or helicopter close to a wall of raindrops and with the sun low in the sky we could see a full circle.
You can produce your own rainbow by having your back to the sun and spraying a hose forward. It shows more clearly if there is a dark background, eg driveway, trees, clouds, or hills shaded from the sun. If you point the hose down and if the sun is low in the sky or if you climb a ladder, you might then observe the full circle of the rainbow, centered on that part of your shadow where your eyes are.
The apparent different curvatures of rainbows are an illusion. They are just different lengths of a fixed circle. When you see a full circle there are no ends of rainbows for pots of gold to hide. And when you, more usually, see an arc (a part of a fixed circle) there are no "ends", just a direction in line with the end. The perceived distance and curvature will depend on where the raindrops are and the background.