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Landscape by Keith Ratcliffe  
© 2009

The Magic of Rainbows

Purring cats, Pink Floyd & rainbows always uplift my spirits and I have taken many pictures of the latter over the years. I learnt about their formation in 'A' level Physics but have only recently fully understood some of their less well known aspects.

The basic optical principle of a rainbow is that light from the sun enters the perfect spheres of tiny rain drops and some of that light comes back out towards the viewer. Different colours of light behave slightly differently when they enter & leave the drop – this is called Dispersion – so we see the separate colours. Incidentally any Pink Floyd fans out there will immediately refer to the cover of “Dark side of the moon” which features a prism showing exactly this effect. In order to see the optical illusion we need to have our backs to the sun, so, the conditions to produce a rainbow are clear sky with sun behind you and looking at a curtain of rain in front of you. This means interestingly that you will never see a rainbow in the Southern sky in the Northern hemisphere.

The arc of the rainbow is always produced at the same angle - 42 degrees -  relative to a line through you and the sun. In order to visualise this aspect imagine looking through a small hole in the top point of a cone whose central axis is pointing back to the sun. Then the extension of the rim of the cone is where the rainbow will be in the sky. A consequence of this fact is that the higher the sun is in the sky, the lower the rainbow. The fullest bows thus occur when the sun is low in the sky i.e. morning and evening and especially low in winter months. Incidentally if the sun is too high you won’t see the main bow at all but may see a feint second bow.

The main arc of a rainbow is formed when the light entering the drop is reflected once off the back face then exits again, however some light goes for a second refection before exiting and this causes the appearance of a second outer bow. This is always less bright and broader and because of the second reflection the colours are reversed. Theoretically the light could be reflected a third & fourth time – in fact an infinity of times each producing a new arc but practically they are so feint as to be invisible.

Rainbow - Dundonnell

An interesting feature occurs particularly with a sharp rainbow against a dark sky - the sharpness being due to a clear edge to the rain and a bright sun. The area within the main bow appears lighter and the area outside it much darker. The light area is a result of the raindrops acting like a giant lens to focus light into the cone that you are looking at thus making it brighter. The darkness is caused by an opposite effect of that area being deprived of light. This latter feature was first observed by Alexander of Aphrodisias in 200 AD and the band now carries his name.

The last fact that I really like about them is this:- we all see a different rainbow. This really sounds quite mystical so what do I mean by the statement? Well the rainbow that each of us sees is produced by our position relative to the sun – remember the line from the sun through your eyes that I referred to earlier, so because no two people can be in exactly the same place, each of our rainbows will be very slightly different. No matter how close two observers get they cannot see the same view. That’s a great one to tell your kids.

I could go on about halos, moonbows & Brocken Spectres but if you want to see some stunning pictures & learn more about these enigmatic optical effects then visit the Atmospheric Optics  Website.

© Keith Ratcliffe
March 2009

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