##
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.