Weather: The heart-uplifting physics of rainbows
Friday 05 December 1997
William Wordsworth's heart may have leapt up when he beheld a rainbow in the sky, but it is doubtful that he fully appreciated the poetic beauty of the physics behind what he was looking at.
The ancient Greeks pondered rainbows a good deal. Aristotle wrote that "the rainbow never forms a full circle, nor any segment greater than a semicircle" (which just goes to show that he had never witnessed one from an aeroplane). "There are never more than two rainbows at one time," he wrote (confirming that he had never seen a rare triple rainbow). "Each of them is three-coloured, the colours are the same in both and their number is the same, but in the outer rainbow they are fainter and their position is reversed."
Aristotle listed the colours of the rainbow as red, green and purple "though between the red and the green an orange colour is often seen" - which sounds odd to anyone brought up on the traditional seven-colour rainbow, though the choice of a number for the colours of the rainbow is arbitrary.
According to some sources, Newton's perception of the spectrum led at first to a six-colour description, but the mystical side of his nature wanted the answer seven - so he added indigo between blue and violet (which had the added virtue of making the ROYGBIV acronym more pronounceable).
A rainbow results from light rays of different colours being refracted different amounts when they pass through a droplet of water. Imagine yourself standing with your back to the sun and a raindrop in the sky in front of you. A ray of sunlight hits the raindrop, is bent as it enters it, and is then reflected off the inside far wall of the rain drop before being bent again as it exits the rain drop, before reaching your eye. For red light, the angle between the light striking the raindrop and the light emerging is 42, while for violet light it is about 40.6. So some raindrops, according to their position, will reflect red light back into your eyes, while others, in different places in the sky, will send other colours of the spectrum to you. And if you draw a line from the sun to your eye, and a line from your eye to the top of the rainbow, the angle between those lines will be 42.
A double rainbow occurs when light has been reflected twice inside the raindrops, like a snooker ball bouncing off two cushions before heading for the pocket of your eye. (The angle for a double rainbow is about 51).
Rainbows look brighter than the sky around them, because they are formed from light emerging from a whole body of raindrops whose three-dimensional mass exaggerates the brightness of a two-dimensional rainbow. If you see a double rainbow, you will notice that the area between the bow is darker than the surrounding sky - the rainbows have stolen much of the light that would naturally fall there. That area is called Alexander's Dark Band, after Alexander of Aphrodisias, who was the first to discuss it, in the second century AD.
The true poetry, however, is that any rainbow depends on the position of the observer. If you see one, it is your personal rainbow, not anyone else's.
Life & Style blogs
Half of young women unable to ‘locate vagina’ and 65% find it difficult to say the word
Is Apple's iCloud safe after leak of Jennifer Lawrence and other celebrities' nude photos?
Reader dilemma: My wife only wants to have sex when she's drunk
Three quarters of the Ikea catalogue is CGI
Anal sex study reveals climate of 'coercion'
Rotherham child sex abuse scandal: Labour Home Office to be probed over what Tony Blair's government knew - and when
What do immigrants really think of Britain? Polish immigrant's Reddit post goes viral
Ashya King: Parents of five-year-old boy refused permission to visit him in hospital and denied bail at Spanish court
With Douglas Carswell joining Ukip, my party has taken another giant step forward
When elitism grips the top of British society to this extent, there is only one answer: abolish private schools
Ashya King: 'Cruel NHS has not given us the treatment we need', says father of five-year-old with brain tumour who fled to Spain
- 1 Al Pacino on suffering from depression: 'It can last and it's terrifying'
- 2 Half of young women unable to ‘locate vagina’ and 65% find it difficult to say the word
- 3 Saudis risk new Muslim division with proposal to move Mohamed’s tomb
- 4 A teacher speaks out: 'I'm effectively being forced out of a career that I wanted to love'
- 5 Mexican woman becomes world’s 'oldest person' at 127
£26000 Per Annum: The Green Recruitment Company: Job Title: SAP Assessor Job T...
£600 - £800 per day: Harrington Starr: Derivatives Risk Commodities Business A...
£600 - £800 per day: Harrington Starr: Power & Gas Business Analyst/Subject Ma...
£100 - £120 per day: Randstad Education Crawley: Year 6 larger then life teach...