page_title: Fraunhofer diffraction equation
section_title: Narrow slits
hierarchical_section_title: Fraunhofer diffraction equation / Slits / Two slits / Narrow slits
caption_attribution_description: English: 2-slit diffraction of red laser light
context_page_description: In optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when the diffraction pattern is viewed at a long distance from the diffracting object, and also when it is viewed at the focal plane of an imaging lens.
  The equation was named in honour of Joseph von Fraunhofer although he was not actually involved in the development of the theory.
  A qualitative discussion of Fraunhofer diffraction can be found elsewhere.
context_section_description: Assume we have two long slits illuminated by a plane wave of wavelength λ. The slits are in the z = 0 plane, parallel to the y axis, separated by a distance S and are symmetrical about the origin. The width of the slits is small compared with the wavelength.
  Solution by integration
  The incident light is diffracted by the slits into uniform spherical waves.  The  waves travelling in a given direction θ from the two slits have differing phases.  The phase of the waves from the upper and lower slits relative to the origin is given by (2π/λ)(S/2)sin θ and -(2π/λ)(S/2)sin θ
  The complex amplitude of the summed waves is given by:
  Solution using Fourier transform
  The aperture can be represented by the function:
  where δ is the delta function.
  We have
  and
  giving
  This is the same expression as that derived above by integration.
  Intensity
  This gives the intensity of the combined waves as:
caption: Two slit interference using a red laser
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