Introduction

We experience the universe almost entirely through light, yet for most of the 19th century physicists treated optics (the study of light) and electromagnetism (the study of electric and magnetic effects) as two separate branches of physics, connected only by coincidence. James Clerk Maxwell changed that. Working from Faraday's law of electromagnetic induction -- the experimentally established fact that a time-varying magnetic field produces an electric field, written $\oint\vec E\cdot d\vec l=-\dfrac{d\Phi_B}{dt}$ -- Maxwell reasoned that nature ought to be symmetric: if a changing $B$-field can create an $E$-field, then a changing $E$-field should, in turn, be able to create a $B$-field. Pursuing this single symmetry argument mathematically, Maxwell was led to predict that coupled, mutually reinforcing electric and magnetic fields could detach from their source charges and propagate through empty space as a self-sustaining wave, travelling at a specific calculable speed: $c=1/\sqrt{\mu_0\epsilon_0}\approx3\times10^8$ m/s. Because this predicted speed matched the already-measured speed of light so precisely, Maxwell concluded that light itself must be an electromagnetic wave -- unifying optics and electromagnetism into a single theory. Nine years after Maxwell's own death in 1879, in 1888, Heinrich Hertz built an apparatus that generated and detected exactly such waves in the laboratory, experimentally confirming the prediction and opening the door to wireless communication, radar and laser technology. This unit develops that whole chain of reasoning: how Maxwell corrected Ampere's law to restore the missing symmetry, how the four resulting equations (Maxwell's equations) mathematically guarantee that electromagnetic waves must exist, what their measurable properties are, how they are produced and detected, and how the full electromagnetic spectrum -- from radio waves to gamma rays, with visible light as only a narrow band in the middle -- is classified and used.