Diffraction grating resolution

December 6, 2013
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Copyright © Michael Richmond. This work is licensed under a Creative Commons License.
  • Even if a beam of light passes through a single slit, the rays within it interfere with each other: we call this diffraction
  • If light rays from different parts of the slit combine on the distant wall after travelling an extra half-wavelength, they interfere destructively and produce a dark spot
  • The pattern produced by light shining through a single slit is a central bright spot, surrounded by dark/light/dark/light spots. The spots become fainter and less distinct the farther away from the center they are.
  • The positions of dark spots on the wall can be determined from the equation

    N lambda sin(theta) = - width where

    theta = angle from the center of the wall to the dark spot N = a positive integer: 1, 2, 3... lambda = wavelength of light width = width of the slit

  • Diffraction causes points of light which are close together to blur into a single spot: it sets a limit on the resolution with which one can see.
  • The smallest angle at which two points of light may be distinguished is

    lambda sin(theta) = - width if the light passes through a rectangular slit, or

    lambda sin(theta) = 1.22 - diameter if the light passes through a circular aperture.

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For more information about diffraction and the limits it places on manufacturing integrated circuits, check out

Source: spiff.rit.edu
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