Speed of Electromagnetic Waves

The result Maxwell obtained. Solving Maxwell's equations for a plane electromagnetic wave travelling through vacuum (again, WBCHSE requires only the RESULT of this calculation, not its derivation) gives an exact expression for the wave's speed, built entirely out of two constants met in earlier chapters -- the permeability of free space $\mu_0$ (which fixes the strength of the magnetic field a given current produces) and the permittivity of free space $\epsilon_0$ (which fixes the strength of the electric field a given charge produces):

A striking numerical coincidence -- or not. Substituting the measured values $\mu_0=4\pi\times10^{-7}\ \text{T m A}^{-1}$ and $\epsilon_0=8.85\times10^{-12}\ \text{C}^2\text{N}^{-1}\text{m}^{-2}$ (Numerical 1 works through the substitution in full) gives $c\approx3.0\times10^8\ \text{m/s}$ -- a value that, when Maxwell first calculated it in the 1860s, matched the ALREADY independently measured speed of light to within the experimental accuracy of the day. Maxwell correctly concluded from this striking agreement that this was no coincidence at all: visible light ITSELF must be an electromagnetic wave, exactly the same physical phenomenon as radio waves or X-rays, differing from them only in wavelength (Section 8.7).

Wavelength and frequency. Like any wave, an electromagnetic wave's speed, frequency $\nu$ (or $f$), and wavelength $\lambda$ are related by the standard wave equation

Since $c$ is the SAME fixed constant for every electromagnetic wave in vacuum (regardless of its frequency), a higher-frequency electromagnetic wave always has a correspondingly SHORTER wavelength, and vice versa -- exactly the relationship used throughout Section 8.7 to convert between the wavelength and frequency of any band of the spectrum (Numericals 2-4 give worked examples). …