The diffraction of a plane wave by an infinite slit. I

The diffraction of a normally incident plane wave by an infinite slit of finite width in a perfectly conducting screen is solved using a Lebedev integral transform theorem and the Wiener-Hopf technique. This technique leads to an infinite system of equations to which the method of successive approximation is applied. In particular, an expression for the transmission coefficient (defined as the ratio of the transmitted to the incident power per unit length) is obtained for $a \ll \lambda$ where $2a$ is the slit width and $\lambda$ is the wave length of the incident wave. There is exact agreement with the known result [3] except for a constant, which has been difficult to determine because of the slow convergence of the series involved; however, a new term has been obtained.