MOTION MOUNTAIN

122 3 what is light?
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intensity per wavelength. If you want to check that white light is a mixture of colours
without any light source, simply hold the lower right-handside of Figure 75 so close to
your eye that you cannot focus the stripes any more. The unsharp borders of the white
stripes have either a pink or a green shade. These colours are due to the imperfections
of the human eye, its so-calledchromaticaberrations.Aberrationshave the consequence
that not all light frequencies follow the same path through the lens of the eye, and thereforetheyhittheretinaat
differentspots.Thisisthesameeffectthatoccursin prismsor
inwaterdropsshowingarainbow.
The left-hand side of Figure 75 explains how rainbows form. Above all, the internal
reflection inside the water droplets in the sky is responsible for throwing back the light
coming from the Sun, whereas the wavelength-dependent refraction at the air–water
surface is responsible for the different paths of each colour. The first two persons to
verify this explanation were Theodoricus Teutonicus de Vriberg (c. 1240 to c. 1318), in
the years from 1304 to 1310 and, at the same time, the Persian mathematician Kamal
al-Din al-Farisi. To check the explanation, they did something smart and simple that
anybodycanrepeatathome. Theybuiltanenlargedwaterdropletbyfillingathinspherical
(or cylindrical) glass container with water; then they shone a beam of white light
through it. Theodoricus and al-Farisi found exactly what is shown in Figure 75. With
this experiment, each of them was able to reproduce the opening angle of the main or
primary rainbow, its colour sequence, as well as the existence of a secondary rainbow,
its observed angle and its inverted colour sequence.* All these rainbows are found in
Figure 56. Theodoricus’s beautiful experiment is sometimes called the most important
contribution of natural science in the Middle Ages.
By the way, the shape of the rainbow tells something about the shape of the water
droplets. Can you deduce the connection?
Incidentally, the explanation of the rainbow given in Figure 75 is not complete. It assumesthatthelightrayhitsthewaterdropletataspecificspotonitssurface.Ifthelight
rayhitsthedropletatotherspots,therainbowsappearatotherangles;however, all those
rainbows wash out. Only the visible rainbow remains, because its deflection angles are
extremal.The primary rainbow is, in fact, the coloured edge of a white disc. And indeed,
the region above the primary bow is always darker than the region below it.
Incidentally, at sunset the atmosphere itself also acts as a prism, or more precisely, as a
cylindrical lens affected by spherochromatism.Therefore, especially at sunset, the Sun is
split into different images, one for each colour, which are slightly shifted with respect to
each other; the total shift is about 1 % of the diameter. As a result, the rim of the evening
Sun is coloured. If the weather is favourable, if the air is clear up to and beyond the
horizon, and if the correct temperature profile is present in the atmosphere, a colourdependentmiragewill
appear:forabout asecondit will bepossibletosee,after ornear
thered, orange and yellow images of the setting Sun, thegreen–blue image, sometimes
even detached. This is the famous green flash described by Jules Verne in his novel Le
*Canyouguesswheretheternaryandquaternaryrainbowsaretobeseen? Therearerarereportedsightings
ofthem;onlytwoorthreephotographsexistworld-wide.Thehunttoobservethefifth-orderrainbowisstill
open. (In the laboratory, bows around droplets up to the thirteenth order have been observed.) For more
details, see the beautiful website at www.atoptics.co.uk. There are several formulae for the angles of the
variousordersofrainbows;theyfollowfromstraightforwardgeometricconsiderations,butaretooinvolved
tobegivenhere.
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net