In this chapter, we introduce Ampere’s lawAmpere’s law of magnetism and Faraday’s law of electromagnetic induction. When Ampere’s law and Faraday’s law are combined with Gauss’ law, \(\nabla \cdot {\mathbf{D}} = \rho\) , and the equation \(\nabla \cdot {\mathbf{B}} = 0\) , expressing the continuity of the magnetic inductionMagnetic induction, the resulting set is known as Maxwell’s equations. This powerful combination of equations can be used to determine the space and time dependence of the electromagnetic field under any set of circumstances. To apply Maxwell’s equations to matter requires that they be supplemented by experimentally determined constitutive relationsConstitutive relations, one linking the electric displacement to the electric field and the other linking the magnetic induction to the magnetic field. With these relations specified, we solve the four Maxwell equationsMaxwell equations for the case of a plane electromagnetic waveWaveelectromagnetic propagating through a dielectric medium. To include the frequency dependence of the electric permittivity of the material through which the wave is propagating in our calculation, we exploit the method of Fourier[aut]Fourier, Jean Baptiste transformsFourier transform. The Fourier transform pair of equations permits us to derive the convolution theoremConvolution theorem, and give mathematical expression to the principle of causalityCausality, which asserts that an effect cannot precede its cause. The law of conservation ofConservation of energy electromagnetic energy is derived. This law leads to the identification of thePoynting vector Poynting vector that governs the propagation of electromagnetic energy through a dispersive mediumDispersive medium. On the basis of a model for the frequency response of a medium, we use the Poynting vectorPoynting vector concept to construct a purely electromagnetic proof of the Beer–Lambert LawBeer – Lambert law of spectrophotometry.