Introduction to the Nature of Light
As we saw in the general introduction to the series of SparkNotes on Optics, the question of the nature of light is the foremost problem in optics. In order to best understand this problem, we must first familiarize ourselves with the concept of a wave and how it behaves. Waves, in fact, have a mathematics all of their own and it will enhance our understanding of optic phenomena if we can apply this mathematical analysis to light. We will also use the fact that the wave equations are linear to argue that light, like all waves, obeys the principle of superposition. This basically means that it you put two waves in the same point in space their amplitudes add up in a simple way.
In the second section we will examine the relationship between light and electricity and magnetism, and see how the propagation of light as a wave comes out of Maxwell's equations for the electric and magnetic fields. This will help us to understand how light propagates through space and how it can transmit energy and momentum. Furthermore, we will use Maxwell's equations to derive the Fresnel Equations, which tell us the proportion of energy which is transmitted and reflected when light is incident on a boundary between media.
In the third section we will combine out treatment of light as a wave and light as an electromagnetic phenomenon by examining what happens when light interacts with matter. This will take us into the topics of dispersion and scattering which will form the basis of our later discussions of more complicated phenomena such as refraction and diffraction. Here it is crucial to remember that although things such as reflection and refraction appear to be rather straightforward, this is because they are a macroscopic manifestation of far more complicated processes occurring on the subatomic level. Scattering, too, seems like a simple concept, but it can help us to answer very basic questions about the world such as "Why is the sky blue?" We will also introduce the related concept of Fermat's Principle, a variational principle, which states that light takes the shortest path between any two points. The implications of this seemingly simple statement are quite profound.