 The grating is a system similar to the single and double slit, but with N parallel slits of width b and distance h.  The system observes the following characteristics:  (Left) Schematic for a grating with 4 parallel slits each of width b and separated by a distance h.  (Right)  Step function for the grating of five parallel slits.        To find the Fraunhofer pattern of this system, the sum of the slits is taken for the Fresnel-Kirchhoff formula.  This results in the following equations: (Fowles, 122) where , and and N is the number of slits in the system.  The intensity distribution for the system then becomes: (Fowles, 123) The factor acts as the envelope for the diffraction pattern.        When the above intensity equation was calculated in Mathematica, we received the following Fraunhofer pattern:  (Left)  Fraunhofer pattern for the grating in 2D.  The inner funtion is the fraunhofer pattern where as the outer function is the diffraction envelope .  (Right)  Fraunhofer pattern in 3D, birds eye view. The Fraunhofer pattern for the grating is the inner pattern with N=3.  The outer function is the envelope defined by .  The width of the inner functions are determined by N.  For larger N, the width of the peaks decreases. 