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.)
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