PROBLEM: I am asked to consider a parallel polarized planar wave with frequency ω is normally incident on a dielectric boundary. The incident time average power flux P_i = 100 w/m^2. The first medium is free space and the second has vaccum permeability but ε=4ε_0. We are also given that the medium is characterized by conductivity σ. I am then asked to find the reflected time average power flux P_reflected in two cases (i) σ/(ω*ε_0)<<1 and (ii) σ/(ω*ε_0)>>1 My problem is that, while performing the calculation I see no use for the quantity in question, namely, σ/(ω*ε_0)... ATTEMPT: I am able to find the reflected time average power flux using P_i = (1/2*η)(E_i)^2 = 100 w/m^2 with P_reflected = (1/2*η)(E_r)^2 and E_r = ρE_i where ρ=(η_2 - η)/(η+η_2). This is especially simple after noting that η_2 = (1/2)η The calculation leads to P_reflected = 100/9 w/m^2 I see no opportunity to consider how varying the conductivity changes that number... I realize that as σ gets big η_2 must go to zero... but we are given a fixed ε=4*ε_0 Am I missing something or is this a poorly posed (or trick) problem??