Weather: The heart-uplifting physics of rainbows

Scarcely anything in nature has excited both scientists and poets as much as rainbows. Yet the physics behind these apparitions has been properly understood only comparatively recently.

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.

sportWWE latest including Sting vs Triple H, Brock Lesnar vs Roman Reigns and The Undertaker vs Bray Wyatt
Arts and Entertainment
Louis Theroux: By Reason of Insanity takes him behind the bars again
tvBy Reason of Insanity, TV review
Arts and Entertainment
Cassetteboy's latest video is called Emperor's New Clothes rap
videoThe political parody genius duo strike again with new video
Arts and Entertainment
tvPoldark, TV review
Have you tried new the Independent Digital Edition apps?
Life and Style
ebookNow available in paperback
ebookPart of The Independent’s new eBook series The Great Composers
  • Get to the point
Latest stories from i100
Have you tried new the Independent Digital Edition apps?
Independent Dating

By clicking 'Search' you
are agreeing to our
Terms of Use.

ES Rentals

    iJobs Job Widget
    iJobs General

    Recruitment Genius: Junior Web Designer - Client Liaison

    £6 per hour: Recruitment Genius: This is an exciting opportunity to join a gro...

    Recruitment Genius: Service Delivery Manager

    Negotiable: Recruitment Genius: A Service Delivery Manager is required to join...

    Recruitment Genius: Massage Therapist / Sports Therapist

    £12000 - £24000 per annum: Recruitment Genius: A opportunity has arisen for a ...

    Ashdown Group: Practice Accountant - Bournemouth - £38,000

    £32000 - £38000 per annum: Ashdown Group: A successful accountancy practice in...

    Day In a Page

    No postcode? No vote

    Floating voters

    How living on a houseboat meant I didn't officially 'exist'
    Louis Theroux's affable Englishman routine begins to wear thin

    By Reason of Insanity

    Louis Theroux's affable Englishman routine begins to wear thin
    Power dressing is back – but no shoulderpads!

    Power dressing is back

    But banish all thoughts of Eighties shoulderpads
    Spanish stone-age cave paintings 'under threat' after being re-opened to the public

    Spanish stone-age cave paintings in Altamira 'under threat'

    Caves were re-opened to the public
    'I was the bookies’ favourite to be first to leave the Cabinet'

    Vince Cable interview

    'I was the bookies’ favourite to be first to leave the Cabinet'
    Election 2015: How many of the Government's coalition agreement promises have been kept?

    Promises, promises

    But how many coalition agreement pledges have been kept?
    The Gaza fisherman who built his own reef - and was shot dead there by an Israeli gunboat

    The death of a Gaza fisherman

    He built his own reef, and was fatally shot there by an Israeli gunboat
    Saudi Arabia's airstrikes in Yemen are fuelling the Gulf's fire

    Saudi airstrikes are fuelling the Gulf's fire

    Arab intervention in Yemen risks entrenching Sunni-Shia divide and handing a victory to Isis, says Patrick Cockburn
    Zayn Malik's departure from One Direction shows the perils of fame in the age of social media

    The only direction Zayn could go

    We wince at the anguish of One Direction's fans, but Malik's departure shows the perils of fame in the age of social media
    Young Magician of the Year 2015: Meet the schoolgirl from Newcastle who has her heart set on being the competition's first female winner

    Spells like teen spirit

    A 16-year-old from Newcastle has set her heart on being the first female to win Young Magician of the Year. Jonathan Owen meets her
    Jonathan Anderson: If fashion is a cycle, this young man knows just how to ride it

    If fashion is a cycle, this young man knows just how to ride it

    British designer Jonathan Anderson is putting his stamp on venerable house Loewe
    Number plates scheme could provide a licence to offend in the land of the free

    Licence to offend in the land of the free

    Cash-strapped states have hit on a way of making money out of drivers that may be in collision with the First Amendment, says Rupert Cornwell
    From farm to fork: Meet the Cornish fishermen, vegetable-growers and butchers causing a stir in London's top restaurants

    From farm to fork in Cornwall

    One man is bringing together Cornwall's most accomplished growers, fishermen and butchers with London's best chefs to put the finest, freshest produce on the plates of some of the country’s best restaurants
    Robert Parker interview: The world's top wine critic on tasting 10,000 bottles a year, absurd drinking notes and New World wannabes

    Robert Parker interview

    The world's top wine critic on tasting 10,000 bottles a year, absurd drinking notes and New World wannabes
    Don't believe the stereotype - or should you?

    Don't believe the stereotype - or should you?

    We exaggerate regional traits and turn them into jokes - and those on the receiving end are in on it too, says DJ Taylor