Diffraction Grating -- from Eric Weisstein's World of Physics

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Diffraction Grating

A diffraction grating is a set of parallel slits used to disperse light using Fraunhofer diffraction. Let there be N slits of width , centered at the origin and separated by a distance d. Then the wavefunction of scalar diffraction theory is given by

where k is the wavenumber and x is the distance from the origin in the direction perpendicular to the slits. Now define the length parameter

then

Using
gives

so the resulting intensity function is given by

Diffraction, Fraunhofer Diffraction, Scalar Diffraction Theory