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1 Physics of rainbows
The rainbow's appearance is caused by dispersion of sunlight as it is refracted by (approximately spherical) rain drops.
The light is first refracted as it enters the surface of the raindrop, reflects off the back of the drop, and is again refracted as it leaves the drop. The overall effect is that the incoming light is reflected back over a wide range of angles, with the most intense light at an angle of about 40°–42°, regardless of the size of the drop. Since the water of the raindrops is dispersive, the amount that the sunlight is bent depends upon the wavelength ( colour) of the light's constituent parts. Blue light is refracted at a greater angle than red light, but because of the light's total internal reflection from the back of the raindrop, the red light appears higher in the sky, and forms the outer colour of the rainbow.
A rainbow does not actually exist as a location in the sky, but is an optical illusion whose apparent position depends on the observer's location. All raindrops refract and reflect the sunlight in the same way, but only the light from some raindrops reaches the observer's eye. These raindrops are perceived to constitute the rainbow by that observer. Its position is always in the opposite direction of the sun with respect to the observer, and the interior is actually a magnified image of the sun, which can be seen to be slightly brighter than the exterior. The bow is centered on the shadow of the observer's head, appearing at an angle of approximately 40°–42° to the line between the observer's head and its shadow (this means that if the sun is higher than 42° the rainbow is below the horizon and cannot be seen unless the observer is at the top of a mountain or a similar vantage point). Similarly it is difficult to photograph the complete arc of a rainbow, which would require an angle of view of 84°. For a 35 mm camera, a lens with a focal length of 19 mm or less would be required, whilst most photographers are only likely to have a 28 mm wide-angle lens. From an aeroplane one has the opportunity to see the whole circle of the rainbow, with the plane's shadow in the centre.
Sometimes, a second, dimmer rainbow is seen outside the primary bow, caused by a double reflection of the sunlight inside the raindrops, and appears at an angle of 50°–53°. Because of the extra reflection, the colours of the bow are inverted compared to the primary bow, with blue on the outside and red on the inside.
A triple rainbow is even more rarely seen. A few observers have reported seeing quadruple rainbows in which a dim outermost arc had a rippling and pulsating appearance.
The first accurate theoretical explanation of a rainbow came from Descartes in 1637. Knowing that the size of raindrops didn't 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 was able to back this up with a derivation of the law of refraction (subsequently, but independently of Snell) and correctly calculated the angles for both bows. However, he was unable to explain the colours.
Isaac Newton was the first to demonstrate that white light was composed of the light of all the colours of the rainbow, which one glass prism could split into the full spectrum of colours, and another could recombine into a beam of white light. He also showed that red light gets refracted less than blue light which led to an essentially complete explanation of a rainbow's optical effect.
2 Rainbows in mythology and religion
The rainbow has a place in legend due to its beauty and the difficulty in explaining the phenomenon before Galileo's treatise on the properties of light.
- In Greek mythology, it is a path made by a messenger ( Iris) between Earth and Heaven.
- The Irish leprechaun's secret hiding place for his crock of gold is usually said to be at the end of the rainbow.
- In Chinese mythology, the rainbow was a slit in the sky sealed by Goddess Nüwa using stones of seven different colours.
- In Hindu mythology, the rainbow is called Indradhanush - meaning the bow of Indra, the God of lightning and thunder.
- In Norse Mythology, a rainbow called the Bifröst Bridge connects the realms of Asgård and Midgård, homes of the gods and humans, respectively.
- In Genesis 9:13 [1], the rainbow is a sign of God's covenant with mankind. After Noah survives the flooding of the earth in the story of Noah's Ark God sent the rainbow to promise that he would never again send such a flood to destroy the world.
