Basic Concepts

I. THE LAWS OF REFLECTION AND REFRACTION
We begin our study of basic geometrical optics by examining how light reflects and refracts at smooth, plane interfaces. Figure 3-1a shows ordinary reflection of light at a plane surface, and Figure 3-1b shows refraction of light at two successive plane surfaces. In each instance, light is pictured simply in terms of straight lines, which we refer to as light rays.
Figure 3-1Light rays undergoing reflection and refraction at plane surfaces

After a study of how light reflects and refracts at plane surfaces, we extend our analysis to smooth, curved surfaces, thereby setting the stage for light interaction with mirrors and lenses— the basic elements in many optical systems.

In this module, the analysis of how light interacts with plane and curved surfaces is carried out with light rays. A light ray is nothing more than an imaginary line directed along the path that the light follows. It is helpful to think of a light ray as a narrow pencil of light, very much like a narrow, well-defined laser beam. For example, earlier in this module, when you observed the passage of a laser beam in a fish tank and visually traced the path of the beam from reflection to reflection inside the tank, you were, in effect, looking at a “light ray” representation of light in the tank.

A. Light rays and light waves

Before we look more closely at the use of light rays in geometrical optics, we need to say a brief word about light waves and the geometrical connection between light rays and light waves. For most of us, wave motion is easily visualized in terms of water waves—such as those created on a quiet pond by a bobbing cork. See Figure 3-2a. The successive high points (crests) and low points (troughs) occur as a train of circular waves moving radially outward from the bobbing cork. Each of the circular waves represents a wave front. A wave front is defined here as a locus of points that connect identical wave displacements—that is, identical positions above or below the normal surface of the quiet pond.