Hi, I have a plane-wave incident upon a planar interface that is perpendicularly polarized with an electric field directed out of the page in the y-hat direction, perpendicular to the x-z plane of incidence. An image of the incident plane: I'm also given the general expressions for the incident, reflected, and transmitted waves for perpendicular polarization: Some relevant eqns (just maxwell equations and solutions): Alright, so what I need to do here is obtain the expressions of E for a parallel polarization, rather than perpendicular. The solution should come from duality, which I assume also comes from maxwell equations. What I do know is that the solution is obtained from the perpendicular incidence of H. Do I simply use the above maxwell equation Del x H = jweE(r), and take the curl of each H(x,z) equation to obtain E for the parallel case? I'm not looking for the solution, but if someone could just point me in the right direction here I'd appreciate it.