Editing Electromagnetic radiation (section)

=== Propagation speed ===
{{Main|Speed of light}}

In empty space (vacuum), electromagnetic radiation travels at the [[speed of light]], <math>c</math>, 299,792,458 meters per second (approximately 186,000 miles per second). In a medium other than vacuum it travels at a lower velocity <math>v</math>, given by a dimensionless parameter between 0 and 1 characteristic of the medium called the [[velocity factor]] <math>\mathit{VF}</math> or its reciprocal, the [[refractive index]] <math>n</math>:  
:<math>v = \mathit{VF} \cdot c = {c \over n}</math>.
The reason for this is that in matter the electric and magnetic fields of the wave are slowed because they polarize the charged particles in the medium they pass through.<ref name="Griffiths">{{cite book| last = Griffiths| first = David J. | title = Introduction to Electrodynamics, Vol. 2| publisher = Cambridge Univ. Press| date = 2017| url = https://books.google.com/books?id=ndAoDwAAQBAJ| isbn = 9781108420419| mr = | zbl = | jfm =}}</ref>{{rp|401}} The oscillating electric field causes nearby positive and negative charges in atoms to move slightly apart and together, inducing an oscillating [[polarization density|polarization]], creating an electric polarization field. The oscillating magnetic field moves nearby [[magnetic dipoles]], inducing an oscillating [[magnetization]], creating an induced oscillating magnetic field. These induced fields, [[superposition|superposed]] on the original wave fields, slow the wave ([[Ewald–Oseen extinction theorem]]). The amount of slowing depends on the electromagnetic properties of the medium, the [[permittivity|electric permittivity]] and [[magnetic permeability]]. In the [[Systeme International|SI]] system of units, empty space has a [[Permittivity of Free Space|vacuum permittivity]] of <math>\epsilon_\text{0} =</math> 8.854×10<sup>−12</sup> F/m ([[farad]]s per meter) and a [[vacuum permeability]] of <math>\mu_\text{0} =</math> 1.257×10<sup>−6</sup> H/m ([[Henry (unit)|henries]] per meter). These universal constants determine the speed of light in a vacuum:
:<math>c = {1 \over \sqrt{\epsilon_\text{0}\mu_\text{0}}}</math>
In a medium that is isotropic and linear, which means the electric polarization is proportional to the electric field <math>\mathbf{D} = \epsilon\mathbf{E}</math> and the magnetization is proportional to the magnetic field <math>\mathbf{H} = {1 \over \mu}\mathbf{B}</math>. The speed of the waves, the <math>\mathit{VF}</math>, and the refractive index are determined by only two parameters: the [[permittivity|electric permittivity]] <math>\epsilon</math> of the medium in farads per meter, and the [[magnetic permeability]] of the medium <math>\mu</math> in henrys per meter<ref name="Griffiths" />{{rp|401}}
:<math>v = {1 \over \sqrt{\epsilon\mu}}</math>
:<math>n = {1 \over \mathit{VF}} = c\sqrt{\epsilon\mu} = \sqrt{{\epsilon\mu \over \epsilon_\text{0}\mu_\text{0}}}</math>
If the permittivity and permeability of the medium is constant for different frequency EM waves, this is called a ''[[dispersion (optics)|non-dispersive]]'' medium.<ref name="Griffiths" />{{rp|417-418}} In this case all EM wave frequencies would travel at the same velocity, and the waveshape stays constant as it travels. However in real matter <math>\epsilon</math> and <math>\mu</math> typically vary with frequency, this is called a ''[[dispersion (optics)|dispersive]]'' medium. In dispersive media different spectral bands have different propagation characteristics, and an arbitrary wave changes shape as it travels through the medium.