Effect of a Water Droplet on a Rainbow

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The Formation of a Rainbow

Sir Isaac Newton found that white light is composed of all wavelengths of visible light. White light is a mixture of all the colors of the spectrum, which are: Red, Orange, Yellow, Green, Blue, Indigo, and Violet. If we break up white light we can see the various components. A glass prism can be used to split white light into various wavelengths. This split occurs because each color in the white light has a different index of refraction. Thus, the different colors will respond differently to the glass. For example, blue light will refract more than the wavelengths corresponding to yellow, and yellow light will refract more than the wavelengths corresponding to red. This effect is called dispersion.

You can see a rainbow whenever you look opposite the sun at sunlit raindrops (or water drops). The raindrop acts like a mirror in that it reflects some of the refracted light back towards you, while other rays leave directly from the opposite side. These refracted rays are the ones that you see as a rainbow.

Thus, when the white light from the sun hits a raindrop the light is dispersed as it enters (like in the prism). The different colors undergo refraction and reflection due to the change of index of refraction between the water and the air.

The formation of rainbows by raindrops was first clearly discussed by Rene Descartes.

Let's assume that the rays from the sun are parallel and that all raindrops are spherical. Of the many paths taken by the rays through a (spherical) water droplet, several rays become concentrated near a minimum deviation angle. These rays enhance the intensity at that particular angle to produce the primary rainbow which we actually see. The ray which is produced at the mini...

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...epends on the size of the raindrops. For very large drops, the width of each color band will be narrow, therefore the various colors do not overlap too much, which results in fairly pure rainbow colors. On the other hand, for small drops each band of color can be so broad that all the colors overlap. This combining of overlapping colors yields a pale or white bow.

References

Greenler, Robert, Rainbows, Halos, and Glories Peanut Butter Publishing 1999

Laven, Philip, Optics of a water drop

Lee, Raymond L., and Fraser, Alistair B., The Rainbow Bridge Penn State Press 2001

Lynch, David K., and Livingston, William, Color and Light in Nature Cambridge University Press 1995

Lynds, Beverly T., About Rainbows

Minnaert, Marcel G. J., Light and Color in the Outdoors Springer-Verlag 1974

Nave, R., Rainbow Concepts

Walker, Jearl, Light from the Sky Scientific American

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