:<math> R_{\|} = \frac{\eta_0\cos\theta - Z_s} {\eta_0\cos\theta + Z_s} </math>
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:<math> R_{\perp} = \frac{Z_s\cos\theta - \eta_0} {Z_s\cos\theta + \eta_0} </math>
where <math>\eta_0 = 120\pi \; \Omega</math> is the intrinsic impedance of the free space.
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Then, the electric and magnetic currents reduce to:
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:<math> \mathbf{J(r)} = \frac{2\eta_0}{\eta_0 + Z} \mathbf{\hat{n} \times H(r)} </math>
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:<math> \mathbf{M(r)} = - \frac{2Z}{\eta_0 + Z} \mathbf{\hat{n} \times E(r)} </math>
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<table>
</table>
Two special limiting cases of an impedance surface are perfect electric conductor (PEC) and perfect magnetic conductor (PMC) surface. For a PEC surface, Z = 0, α = 1, and one can write:
:<math> \mathbf{J(r)} = 2 \mathbf{\hat{n} \times H(r)} </math>