As long ago as in the 3rd-2nd centuries BC, Alexander of Aphrodisias tried to describe the rainbow as a phenomenon involving light and colour; he is regarded as the discoverer of the darker region between the primary and the secondary rainbows.
Aristotle (383-322 BC) was the first one to give a complete description of the optical phenomenon, in Book III of his Meteorology. He proposed that the rainbow is actually an unusual kind of reflection of sunlight from clouds. The light is reflected at a fixed angle. giving rise to a circular cone of "rainbow rays. " In the opinion of Aristotle the rainbow comes into existence in a hemisphere, the centre of which is the observer’s eye and the base of which is the horizontal line,
Ibn al-Haytham (965-1039) treated the formation of rainbow in an article called Maqala fi al-Hala wa qaws quzah. In this article he explained the formation of rainbow as an image, which forms at a concave mirror. If the rays of light coming from a farther light source reflect to any point on axis of the concave mirror, they form concentric circles in that point. When it is supposed that the sun as a farther light source, the eye of viewer as a point on the axis of mirror and a cloud as a reflecting surface, then it can be observed the concentric circles are forming on the axis.
The Persian astronomer and mathematician Qutb Al-Dı ̄n al-Shira ̄zı ̄ (1236–1311) and his pupil al-Fa ̄risı ̄, also known as Kama ̄l al-Dı ̄n (1260–1320), tried to give a first mathematical explanation of the rainbow, which was quite accurate for its age, since it was based on the phenomenon of refraction as described in the Book of Optics by Alhazen.
The angle formed by the rainbow rays and the incident sunlight was first measured in 1266 by Roger Bacon. He measured an angle of about 42 degrees; the secondary bow is about eight degrees higher in the sky.
In 1304 the German monk Theodoric of Freiberg rejected Aristotle's hypothesis that the rainbow results from collective reflection by the raindrops in a cloud. He suggested instead that each drop is individually capable of producing a rainbow. Moreover, he tested this conjecture in experiments with a magnified raindrop: a spherical flask filled with water. He was able to trace the path followed by the light rays that make up the rainbow.
Kama ̄l al-Dı ̄n’s experiments were repeated by Descartes (1596-1650) when he got interested in rainbow. He made some experiments in the light of the sun, with glassy sphere full of water. Standing on foot and directing his back to the sun, he watched through a hole in the glassy sphere, shaking it upward and downward, he finally discovered brightness at the bottom of the sphere. Kama ̄l al-Dı ̄n made similar experiments and obtained the same results as Descartes, many years before him.
In the 17thcentury the rainbow became a strictly physical phenomenon, the object of rigorous investigations according to the law of reflection and refraction.
Rainbow science in history 
