A Rigorous Solution of Two-Dimensional Diffraction Based on the Huygens-Fresnel Principle

The problem of two-dimensional diffraction of light by a slit is solved rigorously on the basis of Huyagens-Fresnel principle assuming the amplitude of a secondary wavelet emitted from an infinite strip of infinitesimal width on the slip aperture to be proportional to cos (θ/2)/√r, where θ is the angle of diffraction and r the distance from the strip. The solution of the problem where a plane-wave of light is normally incident on a slit in a perfectly black screen is expressed in terms of the Fresnel integral. With slight modification, the method is also applicable to the diffraction in a light-absorbing medium.