where θ is the incident angle between the propagation vector of the incident field and the normal to the surface and <math>\eta_0 = 120\pi \; \Omega</math> is the intrinsic impedance of the free space.
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From the surface impedance boundary condition, it can easily be shown that
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:<math> \mathbf{M(r)} = -Z_s \mathbf{\hat{n}\times} \mathbf{J(r)} </math>
In the case of an impedance-matched surface (Z<sub>s</sub> = η<sub>0</sub>), one can write:
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Two special limiting cases of an impedance surface are perfect electric conductor (PEC) and perfect magnetic conductor (PMC) surface. For a PEC surface, Z<sub>s</sub> = 0, R<sub>||</sub> = R<sub>⊥</sub> = -1, and one can write:
:<math> \mathbf{J(r)} = 2 \mathbf{\hat{n} \times H(r)} </math>
:<math> \mathbf{M(r)} = 0 </math>
while for a PMC surface, Z<sub>s</sub> = ∞, R<sub>||</sub> = R<sub>⊥</sub> = 1, and one can write:
:<math> \mathbf{J(r)} = 0 </math>