Demonstrating the Wave Properties of Light From Maxwell’s Equations

Light is one of the many concepts from physics that we still have yet to fully grasp the true nature of due to it having both particle and wave properties. In certain situations it can appear to act as individual particles, whereas in other situations it can appear to act as a wave. This strange behavior of light is known as ‘wave-particle duality’ and is even exhibited by objects other than light such as electrons.

For this article I would like to focus on the wave part of the wave-particle duality by using the fundamental equations from electricity and magnetism, Maxwell’s equations, to demonstrate the wave like properties of light. While it has already been experimentally shown by Young’s infamous double slit diffraction experiment, it turns out that we can also mathematically show the intrinsic wave like properties of light.

Also before moving on, throughout this article I will be assuming an understanding of vector calculus as well as the partial differential equation known as the wave equation so I would recommend reviewing those first.

Maxwell’s Equations and the Wave Equation

To begin, let’s recall what Maxwell’s four equations are. Maxwell’s equations are as follows: