//------------------------------//
// Physics of Rainbows (with ponies) 
// Story: The Art of Rainbow Engineering 
// by Pineta 
//------------------------------//



Despite appearing magical to the uninitiated, rainbows can be explained using relatively simple high school physics. As Twilight explains, the parallel light rays from the sun are refracted when passing from the air into the water droplet, reflected off the far side of the droplet, and refracted again on exiting the drop.

The precise angle by which the raindrops reflect the light depends on the point where the ray enters the drop, but most of the light we see is reflected at around 42 degrees to the incident sunlight. But as Twilight learns, it is also possible for light to be reflected twice inside the drop, giving the secondary rainbow. As it’s reflected twice, the colours are in the opposite order. And as only a smaller amount of light is reflected, it’s considerably fainter.

The angle of refraction can be calculated from the incident angle and the refractive index of the water drop – the speed in air, divided by the speed in water. The separation of the colours occurs because this varies slightly with the wavelength (or colour) of the light.



The angles can be calculated in many ways. One of these, mentioned by Zecora, is the principle of least time. The light ray traveling across a boundary from point A to point B will take the quickest path. A straight line would be the shortest distance, but not the quickest route as it travels a greater distance in the slower medium. If it enters the water slightly to the side, it will increase the path length, but decrease the time taken as it travels a shorter distance in the slower medium.