Jennifer Graham, of Cromwell, asks :-
Many years ago I saw a rainbow with another upside-down sitting on top of it. I have never heard of anyone else reporting this. How could it happen?
John Campbell, a physicist at the University of Canterbury with an interest in optics in the atmosphere, responded.
It could have been a special case for a rainbow or it might have been a sun halo from ice crystals.
A rainbow requires looking towards water droplets (rain, spray, etc) with a bright white source of light (sun, moon, lightning bolt etc) behind you. The rainbow is part of a complete circle at an angle of 42 degrees centred on the line between the sun and our eyes (about four expanded hand-spans at arm's length for the arc).
A rainbow over smooth water could be reflected off the water but would result in two bows (arcs of circles) the same way up but with one centred higher up than the other.
I think the only way to see a rainbow plus an upside down one is if you were looking at rain over very flat water. Then there would also be an upside down rainbow below the normal one. The upside down one would be the lower arc of a rainbow caused by sunlight being reflected off the water and up to the raindrops.
Another possibility is you saw a halo about the sun when there were ice crystals in the cool atmosphere because that sometimes gives the appearance of one "rainbow" with another but inverted "rainbow" above it.
When air cools the water vapour dissolved in it condenses out in liquid form (water). It takes a bit of dust or some other impurity for it to nucleate on. First as fine mist, then clouds, then raindrops. It is more energetically favourable for a drop to grow than another form.
If the higher atmosphere is very cold the water vapour may sublimate into a solid, an ice crystal. Because of the shape of the water molecule it forms a hexagonal crystal which grows outwards at the edges, forming a thin, hexagonal-shaped crystal, either a flat plate or a long needle. These form the thin clouds called cirro-stratus.
A light ray from the sun will enter one edge of the hexagon and, because the speed of light slows down in ice, it emerges from another face having been deviated (by a 60 degree ice prism). Because the speed of light depends on the frequency (colour) of the light the halo is coloured much like a rainbow. The minimum angle of deviation is 22 degrees, half the angle of a water-drop rainbow. Because the sunlight can enter the crystal at all orientations many bows are possible, some appearing upside down. A Russian observer of a 1794 event sketched seven bows forming an overall weird pattern about the sun.
These crystals (thin plate or needle) "float" horizontally if the atmosphere isn't turbulent. When the Sun is low the effect is greatest but the colour display appears only as a rainbow patch on either side of the sun. These are often seen in winter (low sun with cold stable thin high clouds) and are called sun-dogs.
So the basic question to ask is, were you looking away from the sun or towards the sun at the time and was there a possibility of reflection from smooth water?