Multiple Slit Diffraction Pattern
 For an array of  slits of width  and equal spacing  , the intensity of the diffracted light on a screen may be neatly expressed aswhere  is the peak intensity and  is the Chebyshev polynomial of the second kind, which appears when we simplify the ratio  .The parameter  is a normalized wavenumber. It is related to the actual wavenumber  , the perpendicular distance  from the diffraction grating to the screen on which the pattern is observed, and the distance from the center of the pattern  , by  .The formula for the intensity is valid within the Fraunhofer diffraction regime, for which  . In this case, the diffraction pattern is equivalent to the Fourier transform of the diffraction grating. This explains why, since an array of finite-width slits is equivalent to the convolution of an array of delta function slits with a single slit, the resulting diffraction pattern is the product of the two corresponding diffraction patterns.Snapshot 1: for a single, infinitely narrow slit, the diffraction pattern is constant; this is essentially because the Fourier transform of the delta function is constant Snapshot 2: for multiple infinitely narrow slits, there is an infinitely repeating pattern of peaks and troughs, corresponding to constructive/destructive interference between paths from different slits   "Multiple Slit Diffraction Pattern" from The Wolfram Demonstrations Project http://demonstrations.wolfram.com/MultipleSlitDiffractionPattern/ Contributed by: Peter Falloon | ||||||||||||||
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