<P> In Europe, Ibn al - Haytham's Book of Optics was translated into Latin and studied by Robert Grosseteste . His work on light was continued by Roger Bacon, who wrote in his Opus Majus of 1268 about experiments with light shining through crystals and water droplets showing the colours of the rainbow . In addition, Bacon was the first to calculate the angular size of the rainbow . He stated that the rainbow summit cannot appear higher than 42 ° above the horizon . Theodoric of Freiberg is known to have given an accurate theoretical explanation of both the primary and secondary rainbows in 1307 . He explained the primary rainbow, noting that "when sunlight falls on individual drops of moisture, the rays undergo two refractions (upon ingress and egress) and one reflection (at the back of the drop) before transmission into the eye of the observer ." He explained the secondary rainbow through a similar analysis involving two refractions and two reflections . </P> <P> Descartes' 1637 treatise, Discourse on Method, further advanced this explanation . Knowing that the size of raindrops did not appear to affect the observed rainbow, he experimented with passing rays of light through a large glass sphere filled with water . By measuring the angles that the rays emerged, he concluded that the primary bow was caused by a single internal reflection inside the raindrop and that a secondary bow could be caused by two internal reflections . He supported this conclusion with a derivation of the law of refraction (subsequently to, but independently of, Snell) and correctly calculated the angles for both bows . His explanation of the colours, however, was based on a mechanical version of the traditional theory that colours were produced by a modification of white light . </P> <P> Isaac Newton demonstrated that white light was composed of the light of all the colours of the rainbow, which a glass prism could separate into the full spectrum of colours, rejecting the theory that the colours were produced by a modification of white light . He also showed that red light is refracted less than blue light, which led to the first scientific explanation of the major features of the rainbow . Newton's corpuscular theory of light was unable to explain supernumerary rainbows, and a satisfactory explanation was not found until Thomas Young realised that light behaves as a wave under certain conditions, and can interfere with itself . </P> <P> Young's work was refined in the 1820s by George Biddell Airy, who explained the dependence of the strength of the colours of the rainbow on the size of the water droplets . Modern physical descriptions of the rainbow are based on Mie scattering, work published by Gustav Mie in 1908 . Advances in computational methods and optical theory continue to lead to a fuller understanding of rainbows . For example, Nussenzveig provides a modern overview . </P>

What does it mean when there is a rainbow without rain