The real fun of the Maxwell equations comes when we understand the link between electricity and magnetism. A changing magnetic flux can induce currents to flow. This is Faraday’s law of induction. We start this chapter by understanding this link and end this chapter with one of the great unifying discoveries of physics: that the interplay between electric and magnetic fields is what gives rise to light.

Having examined many useful and interesting properties of first static electric fields, then static magnetic fields, and most recently the combination of electric and magnetic fields through the introduction of time-varying effects, we have reached a turning point in our studies. Specifically, we will introduce what is perhaps the most revolutionary concept in electromagnetism: propagation of electromagnetic waves. Electromagnetic waves can carry information and energy, and their properties are described in full using Maxwell’s Equations. We will explore these properties in detail in this and the following chapters.

We have introduced Gaussian optics and used a matrix formalism to describe light rays through optical systems in Chapter 1. Light rays are based on the particle nature of light. Since light has a dual nature, light is waves as well. In 1924, de Broglie formulated the de Broglie hypothesis, which relates wavelength and momentum. In this chapter, we explore the wave nature of light, which accounts for wave effects such as interference and diffraction.