We can simplify the above n to a familiar form of the index of refraction of a linear isotropic dielectric. To do so, we remember that in a linear dielectric an applied electric field E induces a polarization P proportional to the electric field P = ϵ ϵ 0 χ χ e E . When the electric field changes, the induced charges move and produces a current density given by ∂ ∂ P / ∂ ∂ t . Since the time dependence of the electric field is exp ⁡ ⁡ ( − − i ω ω t ) , we get J = − − i ϵ ϵ 0 ω ω χ χ e E , which implies that the conductivity σ σ = − − i ϵ ϵ 0 ω ω χ χ e .