You may see a hundred rainbows in a week around this time of year but you will never see one at the stroke of noon. Neither, here in Ireland, will you observe one to the south. And there are more constraints: a morning rainbow appears al- ways in the western sky, while an evening rainbow is always in the east.
To form a rainbow, millions of little raindrops act like tiny mirrors. But rather than being reflected on the surface, the light passes into each drop to be reflected from the back, and the optical properties of a sphere of water are such that the angle of reflection is always 42 degrees. This 42-degree angle limits the occurrence of the rainbow: none will appear unless the drops are located in the sky in precisely such a way that the eye can catch the light reflected at this angle. As a result, the bow is part of a circle which has an angular width of 42 degrees. The centre of this circle is at what is called the anti-solar point - a point on the continuation of an imaginary line joining the sun and the observer's head, and which is as far below one horizon as the sun is above the other.
A second consequence of reflection within the water drop is that the light, as it passes from air to water and out again, is separated into its constituent colours. The eye picks up different colours from different strategically placed drops, giving the rainbow its familiar pattern with violet on the inside and red on the outer edge.
These short rules and few provide the key to the constraints. Firstly the rainbow must always be on the opposite side of the sky from the sun - hence the location of the morning and evening rainbows. Secondly, in the northern hemisphere the sun is never in the north, so a rainbow can never appear to the south. And thirdly, if the sun is more than 42 degrees above the horizon - as it is during late spring and summer around noon - the imaginary anti-solar point will be more than 42 degrees below the opposite horizon, and the rainbow's arc will not be visible; in a sense, the arc can be imagined as lying entirely below the horizon.
There are, of course, two further requirements for a rainbow: water-drops and sunlight. Rainbows occur, therefore, when breaks in the cloud allow the sunbeams through and when, simultaneously, a passing shower provides a curtain of rain on the opposing skyline.