![]() The colours of the rainbow are primarily due to refraction and dispersion of light by the raindrops, but the correct explanation is somewhat involved. A Gaussian distribution has been assumed, mean diameter 0.5 mm, standard deviation 0.06 mm.įor details of the computation of the above figures see the section on Mie scattering. If the drop-sizes are not very uniform, the interference fringes (supernumerary bows) are washed out.Ĭomputed colours for a mixture of different droplet sizes. The scale gives the angle, measured from the point opposite to the sun.ĭroplet diameters, from top to bottom: 2 mm, 1 mm, 0.7 mm, 0.5 mm From the appearance of the bow, one can get a fair estimate of the average diameter of the drops. ![]() The following pictures show the colours of the rainbow, computed for different drop sizes. Light that is twice reflected before it leaves the drop produces the second bow. The fact that from each drop two beams reach the eye and are added there, causes the interference fringes seen at the inner side of the bow in the pictures below. What we see as a rainbow are the tiny, but (in the light of the sun) very bright reflections in the innumerable falling drops. Then green becomes bright and vanishes, and finally red (right image). As the shortest waves are refracted most, first the "blue" rays join and get bright while green and red are still separated. Increasing the angle of observation (measured from the point opposite to the sun), the two reflections approach each other (middle image), join while becoming very bright – and eventually vanish. The left image shows a drop well inside of the rainbow, where the sky is brighter than outside. The sketch to the left corresponds to the image just below it. This can happen along two different paths, and correspondingly two reflexes are seen on the left side of the drop. Light which enters the drop is reflected at the back surface and leaves the drop to finally reach the eye of the observer. Instead of the sun, a small lamp shines on the drop, its mirror image on the front surface is seen as a white point to the right of the centre. Here these shall be considered too.Ī water-filled spherical vase serves as a model for a falling raindrop (following Antonius de Dominis, Descartes and Goethe). – and many more also the geometric-optical explanation is to be found at several places, while interference and diffraction phenomena in most cases are only mentioned. (There is a special section devoted to Mie scattering.)īeautiful images of rainbows and other atmospheric phenomena may be found in the web at the following sites: Gustav Mie finally in 1908 presented the exact solution for the scattering of light by dielectric spheres – a solution which nowadays can be evaluated with fast computers, but which does not give an intuitive explanation for the calculated phenomena. ĭescartes gave 1637 the explanation on the basis of ray optics (geometric optics),ġ838 to give a detailed (but approximate) description including diffraction and interference effects. Seneca hit on the lucky idea that it might be an infinite repetition of the sun's image.Īntonius de Dominis realises first, what exactly happens in each single drop.ĭescartes develops in more detail than the latter the reflection which is connected with refraction, and by this explains the second bow. We skip what else the ancient have thought or said. ![]() In the oldest times the iris was believed to be a reflection of the sun in a dark cloud. Goethe, in a section on the rainbow of his treatise on colours (Farbenlehre) sketches the historic progress of insight: ![]() ( More pictures)Ī very conspicuous phenomenon with a not-so-simple explanation, the rainbow, comes from reflection and refraction of the sunlight in the falling drops its colours are mainly due to dispersion, which means that the refractive index of water depends on the wavelength of light. Rainbow, Hannover, August 29th 2006, 19:33 CEST.
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