How does light travel?

Understanding how and where a rainbow appears is tied to understanding how light travels. In this section we will investigate some of the basic theories about the nature of light.

To help with geometric understanding, we will assume that light travels in rays. We begin with light rays moving through the air at a constant speed and consider the reflection of light. In 1657 the mathematician Pierre de Fermat postulated a simple principle:

Light follows a path that minimizes total travel time.

Figure 1: The reflection of light from a smooth surface.

Question 1

Using Fermat's Principle, Figure 1, and calculus, determine the relationship between the incoming and outgoing angles.
Thus you have discovered a relationship between the angles formed by incoming and outgoing rays of reflected light. We call a the angle of incidence and b the angle of reflection. In the last part of Question 1 you deduced the Law of Reflection: the angle of incidence is equal to the angle of reflection. It is also possible to demonstrate the Law of Reflection completely geometrically.
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Frederick J. Wicklin <>
Paul Edelman <>

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

Last modified: Tue Oct 24 15:02:39 1995