Low-frequency scattering by a slit in a conducting plane

The problem of diffraction of an H polarized plane wave by a narrow slit in a perfectly conducting screen can be formulated as an integral equation with a Hankel function difference kernel. For narrow slits, we replace the Hankel function by the first three terms of its series expansion and solve exactly the resultant integral equation. The results are superior to those obtained by solving a succession of integral equations, each with a static kernel, which is the traditional approach. Also solved is the slightly more difficult problem of E polarization. We indicate that the method can be generalized to include more terms in the kernel expansion, to diffraction by multiple slits, with different media and with impedance boundary conditions on the screen.