PHGN462: Advanced E&M Quiz 2 – September 21, 2009 NAME: 1. Consider s-polarized electromagnetic radiation incident on a flat interface between two linear materials, labeled 1 and 2, with each characterized by the constants: {i , µi , ni }. As usual define {θi , θr , θt } to be the angles of incidence, reflection, and transmission, respectively, with respect to the normal to the interface. Use the coordinate system shown in the figure. kr y ki 1 z (out) x 2 kt a. Assume that the s-polarized electric field is in the ẑ-direction (out) as shown in the figure for all the waves at some instant of time. On the figure draw the corresponding magnetic field vector for each wave. ~ 0α , B ~ 0α } be the field amplitudes for α = {i, r, t}. Assuming there are no free charges or currents, write down b. Let {E the boundary conditions at the interface associated with all four of Maxwell’s equations (one of them will be trivial, 0=0). ~ 0α = nα (k̂α × E ~ 0α ), to show that the boundary condition associated with Maxwell’s second c. Use the condition, B c equation is equivalent to that associated with Maxwell’s third equation. (This leaves two independent linear equations which you solved as part of your homework. DO NOT solve them here.) 1

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