Light – discussion

From Mamxwell’s equations for the speed of light in vacuum we can derive the formula c₀ = (ε₀μ₀)^-1/2, where ε₀ and μ₀ are the permittivity and permeability of vacuum. Maxwell’s equations and the derived results are exactly valid only for vacuum, of course. To extend Maxwell’s equations likewise to a medium, empirical material coefficient of relative permittivity ε_r and of relative permeability μ_r are defined. Using them the hypothetical speed of light takes the form
c = (ε_rμ_r)^-1/2(ε₀ μ₀)^-1/2. Refractive index n is defined as a ratio of speed of light c₀ in vacuum to that c in a medium n = c₀/c, so that refractive index of a medium takes the hypothetical value of n = (ε_rμ_r)^1/2.

Permeability μ_r = 1 and permittivity ε_r = 81 are the values for water found with static electrical measurements. So, calculated hypothetical value of refractive index is n = 9, but an experimental value is n = 1,33. Great discrepancy between the hypothetical and experimental values has its explanation in a groundless extrapolation of the relative permittivity for light.

We illustrate the relative permittivity in Fig. 23. The greater circles depict the free charge Q originated from the voltage source V. Between the two electrodes there is a dielectric, which is represented by its dipoles illustrated by small circles. Dipoles are polarised by an applied electric field of intensity E₀ originated by a free charge Q. Inside the dielectric body, charges of dipoles mutually cancel their effect. At the electrodes the dipole charges (labelled bound charges) are uncompensated and create field of intensity E_d, which together with E₀ forms the final intensity E = E₀ – E_d.

Fig. 23 Relative permitivity ε_r

As the bound charges weaken the effect of the free charges Q, the size of Q is larger than it would be q in case of absence of the dielectric. The material constant of the relative permittivity is the ratio of the free charges between two electrodes with dielectric and without it ε_r = Q/q.

Per definition, photon travels at a speed c₀ of light in vacuum. Its path in a material takes a zigzag form due to the interaction between the photon and electrons and the average time of travelling is prolonged. This is the reason why the speed c of light is slower in a material.

At last it should be sad why the relation c₀ = (ε₀μ₀)^-1/2 is valid exactly. This relationship, which can be derived from the Maxwell’s equations, has been recommended (1948) as a definition for the vacuum permittivity within the SI system of units by The General Conference on Weights and Measures (Conférence Générale des Poids et Mesures, CGPM) and has been legitimised in most of states. The value of permittivity results from the following decisions:

a) The current unit Ampere is defined as “the constant current that will produce an attractive force of F = 2 × 10^-7 newton per meter of length between two straight, parallel conductors of infinite length and negligible circular cross section placed one meter apart in vacuum”.

b) The rationalised form of Maxwell’s equations is legitimised. Here the permeability of vacuum acquires value of μ₀ = 4π10^-7 [mkgs^-2A^-2], which follows from the Ampere’s force law
F = μ₀ I₁I₂L/2π when the above quoted force F is substituted.

c) The value of the permittivity makes up from the equation
ε₀ = (μ₀c₀)^-1/2 = 8,854 10^-12 [kg^-1m^-3s⁴A^-2].

The vacuum permeability μ₀ and the permittivity ε₀ are measurement system constants, they do not describe a physical property of the vacuum. Their value is determined by above quoted decisions. Only their product ε₀μ₀ is a physical constant that can be measured because it is tied to speed of light by the equation c₀ = (ε₀μ₀)^-1/2.