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.

News
Russia Today’s new UK channel began broadcasting yesterday. Discussions so far have included why Britons see Russia as ‘the bad guy’
news

New UK station Russia Today gives a very bizarre view of Britain

News
people
News
people
Voices
Left: An illustration of the original Jim Crowe, played by TD Rice Right: A Couple dressed as Ray and Janay Rice
voices

By performing as African Americans or Indians, white people get to play act a kind of 'imaginary liberation', writes Michael Mark Cohen

PROMOTED VIDEO
Have you tried new the Independent Digital Edition apps?
Life and Style
ebooksA superb mix of recipes serving up the freshest of local produce in a delicious range of styles
Life and Style
ebooksFrom the lifespan of a slug to the distance to the Sun: answers to 500 questions from readers
Arts and Entertainment
Keira Knightley and Benedict Cumberbatch at the premiere of The Imitation Game at the BFI London Film Festival
filmsKeira Knightley tried to miss The Imitation Game premiere to watch Bake Off
News
i100
Arts and Entertainment
Hand out press photograph/film still from the movie Mad Max Fury Road (Downloaded from the Warner Bro's media site/Jasin Boland/© 2014 Warner Bros. Entertainment Inc.)
films'You have to try everything and it’s all a process of elimination, but ultimately you find your path'
Arts and Entertainment
Imelda Staunton as Dolores Umbridge in the Harry Potter films
books

New essay by JK Rowling went live on Pottermore site this morning

News
people

Top Gear presenter is no stranger to foot-in-mouth controversy

News
i100
Latest stories from i100
Have you tried new the Independent Digital Edition apps?
Independent Dating
and  

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

ES Rentals

    iJobs Job Widget
    iJobs General

    Mobile Developer (.NET / C# / Jason / Jquery / SOA)

    £40000 - £65000 per annum + bonus + benefits + OT: Ampersand Consulting LLP: M...

    Humanities Teacher - Greater Manchester

    £22800 - £33600 per annum: Randstad Education Manchester Secondary: The JobAt ...

    Design Technology Teacher

    £22800 - £33600 per annum: Randstad Education Manchester Secondary: Calling al...

    Foundation Teacher

    £100 - £125 per day: Randstad Education Chelmsford: EYFS Teachers - East Essex...

    Day In a Page

    The drugs revolution starts now as MPs agree its high time for change

    The drugs revolution starts now as MPs agree its high time for change

    Commons debate highlights growing cross-party consensus on softening UK drugs legislation, unchanged for 43 years
    The camera is turned on tabloid editors in Richard Peppiatt's 'One Rogue Reporter'

    Gotcha! The camera is turned on tabloid editors

    Hugh Grant says Richard Peppiatt's 'One Rogue Reporter' documentary will highlight issues raised by Leveson
    Fall of the Berlin Wall: It was thanks to Mikhail Gorbachev that this symbol of division fell

    Fall of the Berlin Wall

    It was thanks to Gorbachev that this symbol of division fell
    Halloween 2014: What makes Ouija boards, demon dolls, and evil clowns so frightening?

    What makes ouija boards and demon dolls scary?

    Ouija boards, demon dolls, evil children and clowns are all classic tropes of horror, and this year’s Halloween releases feature them all. What makes them so frightening, decade after decade?
    A safari in modern Britain: Rose Rouse reveals how her four-year tour of Harlesden taught her as much about the UK as it did about NW10

    Rose Rouse's safari in modern Britain

    Rouse decided to walk and talk with as many different people as possible in her neighbourhood of Harlesden and her experiences have been published in a new book
    Welcome to my world of no smell and odd tastes: How a bike accident left one woman living with unwanted food mash-ups

    'My world of no smell and odd tastes'

    A head injury from a bicycle accident had the surprising effect of robbing Nell Frizzell of two of her senses

    Matt Parker is proud of his square roots

    The "stand-up mathematician" is using comedy nights to preach maths to big audiences
    Paul Scholes column: Beating Manchester City is vital part of life at Manchester United. This is first major test for Luke Shaw, Angel Di Maria and Radamel Falcao – it’s not a game to lose

    Paul Scholes column

    Beating City is vital part of life at United. This is first major test for Shaw, Di Maria and Falcao – it’s not a game to lose
    Frank Warren: Call me an old git, but I just can't see that there's a place for women’s boxing

    Frank Warren column

    Call me an old git, but I just can't see that there's a place for women’s boxing
    Adrian Heath interview: Former Everton striker prepares his Orlando City side for the MLS - and having Kaka in the dressing room

    Adrian Heath's American dream...

    Former Everton striker prepares his Orlando City side for the MLS - and having Kaka in the dressing room
    Simon Hart: Manchester City will rise again but they need to change their attitude

    Manchester City will rise again but they need to change their attitude

    Manuel Pellegrini’s side are too good to fail and derby allows them to start again, says Simon Hart
    Isis in Syria: A general reveals the lack of communication with the US - and his country's awkward relationship with their allies-by-default

    A Syrian general speaks

    A senior officer of Bashar al-Assad’s regime talks to Robert Fisk about his army’s brutal struggle with Isis, in a dirty war whose challenges include widespread atrocities
    ‘A bit of a shock...’ Cambridge economist with Glasgow roots becomes Zambia’s acting President

    ‘A bit of a shock...’ Economist with Glasgow roots becomes Zambia’s acting President

    Guy Scott's predecessor, Michael Sata, died in a London hospital this week after a lengthy illness
    Fall of the Berlin Wall: History catches up with Erich Honecker - the East German leader who praised the Iron Curtain and claimed it prevented a Third World War

    Fall of the Berlin Wall

    History catches up with Erich Honecker - the East German leader who praised the Iron Curtain and claimed it prevented a Third World War
    How to turn your mobile phone into easy money

    Turn your mobile phone into easy money

    There are 90 million unused mobiles in the UK, which would be worth £7bn if we cashed them in, says David Crookes