page_title: Diffraction formalism
section_title: A simple quantitative description
hierarchical_section_title: Diffraction formalism / Diffraction from an array of narrow slits / A simple quantitative description
context_page_description: Diffraction processes affecting waves are amenable to quantitative description and analysis. Such treatments are applied to a wave passing through one or more slits whose width is specified as a proportion of the wavelength. Numerical approximations may be used, including the Fresnel and Fraunhofer approximations.
context_section_description: Multiple-slit arrangements can be mathematically considered as multiple simple wave sources, if the slits are narrow enough. For light, a slit is an opening that is infinitely extended in one dimension, and this has the effect of reducing a wave problem in 3D-space to a simpler problem in 2D-space. 
  The simplest case is that of two narrow slits, spaced a distance  apart. To determine the maxima and minima in the amplitude we must determine the path difference to the first slit and to the second one. In the Fraunhofer approximation, with the observer far away from the slits, the difference in path length to the two slits can be seen from the image to be
  Maxima in the intensity occur if this path length difference is an integer number of wavelengths.
  The corresponding minima are at path differences of an integer number plus one half of the wavelength:
  .
  For an array of slits, positions of the minima and maxima are not changed, the fringes visible on a screen however do become sharper, as can be seen in the image.
caption: Diagram of a two slit diffraction problem, showing the angle to the first minimum, where a path length difference of a half wavelength causes destructive interference.