The Physics of a Rainbow



So some of you might be wondering, what exactly is a rainbow? We all enjoy spotting one in the sky on those rare occasions but few of us know why it got there in the first place. A rainbow can be described as a charming chromatic dispersion. It is formed when white sunlight is intercepted by a drop of water in the atmosphere and some of the light refracts into the drop, reflects from the drop's inner surface, and then refracts out of the drop. The first refraction separates the first refraction separates the sunlight into its component colors and the second refraction increases the separation ultimately resulting as a rainbow. Colors of a rainbow are caused by the refraction and internal reflection of light rays that enter the raindrops. The concentration of rays near the minimum deviation gives rise to the arc of the rainbow. The incoming ray is unpolarized, and can be represented by two polarized waves whose plans of polarization are perpendicular to each other. There a few things that can happen to the ray when entering atmosphere. Part of the incoming ray is reflected back to the atmosphere; part of the light refracts into the drop and then refracts back to the atmosphere; some reflect from the drop’s inner surface and refract back to the atmosphere. Ultimately this refraction of rays give rise to an ordinary rainbow. In some cases, some rays will reflect twice inside the drop and then refract back to the atmosphere which ultimately gives rise to a secondary rainbow.
Rainbows briefly can be described as an optical and meteorological phenomena which cause a spectrum of light to appear in the sky when the sun shines onto droplets of moisture in the Earth’s atmosphere. As a result one can see a multicolored arc with red on the outside and violet on the inner arc. In most cases the spectrum of colors usually result in a sequence of Newton’s sevenfold red, orange, yellow, green, blue, indigo, violet or also known as Roy G. Biv.
A secondary rainbow can be seen on rare occasions outside the primary arc with colors in the opposite order. Though rainbows are usually bow-shaped, there are also phenomena of rainbow-colored strips in the sky: in the shape of stripes, circles or even flames
The rainbow is actually a disk of scattered light, but it is brightest at the edge; the disk for different wavelengths is a different size, and that is why we see the color effects there.When light refracts, it follows the law of refraction ni sin(ctai)=nr sin( ctar) where n is the index of refraction. There is an angle of incidence and an angle of refraction. Most of the light is refracted out by one ray. When your eyes intercept the separated colors from the raindrops the red color you experience is the product of when drops are angled slightly higher in the sky than when you experience seeing blue. 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 40-42 degrees. The angle is independent of the size of the drop but does depend on its refractive index. For instance, seawater has a higher refractive index than rain water therefore the radius of a rainbow in the sea spray is smaller than an actual rainbow. It becomes visible to the eye due to a misalignment of these bows.