2 Optical Spectrum. Refraction, reflection, attenuation and dispersion
2.1 Introduction

Light as an electromagnetic wave is characterised by a combinations of time-varying E (electric field) and H (magnetic field) propagating through space according to the Maxwell equations introduced by James Clerk Maxwell in the late 19th century.

Light can be characterized using several spectral quantities, such as frequency, υ,

(001) , where ω is the angular frequency or wavelength λ,

(002) , being c the speed of light in vacuum

c is a universal physical constant and its value is exactly 299 792 458 m/s.

Usually a value of c= 3 108 m/s is used as a good approximation.

In any other medium different of vacuum, the light phase velocity, v (the speed at which the crests or the phase of the wave moves), depends on the refractive index, n, of the medium as follows [2] :

(003) , where n can be defined by the following equation:

(004) , being εr and μr the relative electrical permittivity and magnetic permeability of the medium respectively [3]. The refractive index is a function of the wavelength.

The relationships among electricity, magnetism, and the speed of light in a medium are summarized by the following equation:

(005)

Wave-particle duality: Every elementary particle or quantic entity exhibits the properties of not only particles, but also waves. Electromagnetic radiation propagates following linear wave equations, but can only be emitted or absorbed as discrete elements: Photons, thus acting as a wave and a particle simultaneously.

The energy of a photon, E, is proportional to its frequency,υ, and can be calculated by using the Planck–Einstein relation also known as Planck equation [4] :

(006)

where h is the Planck’s constant, = 6.62·10–34 Js or 4.1356·10–15 eVs.

The constant: hc = 1.24 eVμm.

The value of the relative permittivity of silica (silicon dioxide: SiO2) is εr = 3.9, and the relative magnetic permeability of SiO2 is μr = 0.53. Calculate the refractive index of silica.

SOLUTION

The refractive index of SiO2 is: (007)