# Diffraction due to a long narrow slit

I wanted to derive an expression for intensity due to a single slit whose dimensions are 1m and a ( where a is of the order of wavelength (diffraction. For that firstly I divided the slit into infinite number of linear sources and than consider an arbitrary linear source. Now I can find the electric field contribution due to this source easily if I assume that the dimensions of slit are dx ( as it is at distance x from center of slit) and a. Where a is nearly of thr order of wavelength. Now I can find electric field contribution due to it by using approximation that the rays which come parallel from the points of linear source will intersect because a is very small. Now after finding the contribution due to a linear source of width dx, I would try to find electric field due to a long linear source. For a rectangular aperture of small dimension it is easier because parallel rays may be approximated to intersect. But when the slit length is finite like 1m and width is of order of wavelength. Than it gets difficult because now intersecting rays from various Infinitesimal linear sources will not be parallel. And the approximation that we use for path difference for parallel rays is no longer valid because these linear sources will not emmit parallel rays to intersect. Can someone help me to find the derivation ? I know that the intensity along the length of the slit will be almost constant because light will be diffracted along the width a. But I want to proof this statement . Sorry...if the question has gone too long