The far-zone field scattered by a narrow conducting strip located at the interface between two semi-infinite dielectric half-spaces is determined analytically. The permeabilities of the two half-spaces are equal, and the excitation is restricted to be transverse magnetic to, and invariant along, the axis of the strip. The solution of the approximate integral equation for the current on the strip is constructed as an infinite series of Chebyshev polynomials of the first kind weighted by a function exhibiting the proper edge behavior at the strip edges. Two methods, one depending upon integrals of the known excitation and the other upon its derivatives, are presented. The far-zone scattered field is represented as series involving Bessel functions and coefficients determined from the excitation. In the special case of incident plane wave illumination, explicit expressions for the series coefficients are given.