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The electric field in a narrow slot in a conducting screen between two half-spaces of different electromagnetic properties and the far-zone diffracted field are determined analytically. Both transverse electric and transverse magnetic excitations are considered, and the slot electric field in each case is obtained by solving the corresponding narrow-slot integral equation by two methods. In both methods the solutions are expressed as the product of a weight function and a series of Chebyshev polynomials. The series coefficients depend upon an integral of the known excitation in one method, while in the other they depend upon its derivatives. The solution procedure is illustrated by an example in which the excitation is taken to be a uniform plane wave.