Our analysis does not yet explain why the rainbow has different colors or why it appears as an arc. We ask you to think about these two questions here, in conjunction with the data you gathered in Experiment #3.

Figure 5: Light hitting water droplets is refracted and reflected into an observer's eyes. Each color of light is most tightly focussed when it comes from a certain angle, which corresponds to the "rainbow angle" for that color.

Question 11

Give a geometric explanation why the rainbow looks like part of a circle.
Recall that different colored light travels at different speeds through water so that, for instance, the index of refraction for red light in water is about 1.3318 and for violet light it is 1.3435. Rainbows have colors because water refracts different wavelengths of light slightly differently. Red, yellow, and violet light have wavelengths around 700, 550, and 400 nanometers respectively.

Question 12

Explain why red appears on the "top" of the rainbow and violet appears on the bottom. Based on the results of Experiment #3 and Figure 5, construct a geometric model that describes how rainbows are formed when the sun is behind an observer.

For additional information about rainbows, including historical facts and a bibliography, see the URL

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Frederick J. Wicklin <>

This lab is based on a module developed by Steven Janke and published in Modules in Undergraduate Mathematics and its Applications, 1992.

Last modified: Mon Dec 18 16:43:18 1995