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The scattering of a plane electromagnetic wave of wave number , by an infinite slit (of width ) formed by two unidirectionally conducting, semi-infinite coplanar screens of zero thickness is considered. By employing an integral equation procedure, a rigorous asymptotic solution is obtained up to order . The currents induced on the screens and the first few terms in the transmission coefficient are evaluated. The similarity between this and the corresponding problem involving perfectly conducting screens is pointed out.