# Conclusions

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
`http://www.unidata.ucar.edu/staff/blynds/rnbw.html`

**Previous:** Analysis of experiment

**Return to:** Outline

Frederick J. Wicklin <fjw@geom.umn.edu>
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