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Consortium for Mathematics and its Applications

Product ID: 99724
Supplementary Print
Undergraduate

Somewhere Within the Rainbow (UMAP)

Author: Steven Janke


This module uses Fermat's least-time principle for the path of light to derive the laws of reflection and refraction, and then analyzes the passage of light through a raindrop to explain quantitatively the phenonmenon of the rainbow. An appendix is included, which treats diffraction theory.

Table of Contents:

THE PROBLEM: EXPLAINING THE RAINBOW

SOME EARLY HISTORY

REFLECTION

REFRACTION

THE RAINBOW ANGLE

COLORS

THE SECONDARY BOW

FURTHER DIRECTIONS

APPENDIX
The Wave Nature of Light
The Diffraction Theory of the Rainbow

SOLUTIONS TO THE EXERCISES

REFERENCES

ACKNOWLEDGMENTS

ABOUT THE AUTHOR

©1999 by COMAP, Inc.
UMAP Module
25 pages

Mathematics Topics:

Calculus

Application Areas:

Physical Sciences , Optics, Meteorology

Prerequisites:

Derivatives of sine and cosine; finding maxima and minima by setting the derivative to zero; testing critical points by using the second derivative test

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