Dielectric interface. The x-y plane is the interface between two essentially infinite dielectric slabs. Each dielectric is uniformly polarized. P = P1 k for z 0. (a) Determine , the surface density of bound charge at the interface. Give your answer in terms of P1 and P2. (b) Assume that the dielectrics are both linear. The one below the x-y plane has susceptibility 1; the one above, 2. Determine E1 and E2 the electric fields inside the two dielectrics. Give your answer in terms of P1, P2, 1, 2, 0 and k. (c) What is the total charge density tot of the interface? Give your answer in terms of P1, P2, 1, 2 and 0. (d) Now assume that there is no free charge at the interface. Determine P2 in terms of P1, 1 and 2. Figure 2: Note: This figure is not directly related to the problem. However the kind of inter- face analysis carried out here is relevant to understanding the kinds of photonic structures shown here. Advances in fabrication now make it possible to make complex structures with features on the micron scale. The figure shows schematics