1. The problem statement, all variables and given/known data A plane wave is incident at 70˚ to surface normal traveling within a medium with relative permittivity = 4, striking the boundary with air. Where is the nearest magnetic field max. to the boundary in the initial medium? Find the 1/e penetration depth of the evanescent wave. 2. Relevant equations No equations are given, but i've been using: θC= sin-1(εr2/ εr1)^.5 3. The attempt at a solution For the second part, i said that in the air, Et and Ht vary with the factor: exp(-α2z)exp(-jβ2xx), where α2 = β2(εr1/ εr2*sin2θi-1)^.5 = 1.59β2 the 1/e penetration distance is then just z = 1/(1.59β2) = .628β2 The first part, however, is where I am having my main difficulty. I think I know how to do it were this to be a plane wave incident on a conductor, but I am not sure if I can use the same logic for the air interface given that I don't think I can assume that E = 0 at the boundary. ( for a conductor, i've been able to solve for H for a TE wave being H1=2*Ei0/Z1*cos(β1zcosθi)*exp(-jβ1xsinθi) from here I would just find where β1zcosθi = 0 and that would give the max. Does this still work for an air incidence though? And is there any max for a TM wave? Any help would be greatly appreciated! Thanks!