Editing Wavelength (section)

=== Single-slit diffraction ===
{{Main|Diffraction|Diffraction formalism}}
[[File:Double-slit diffraction pattern.png|thumb|200px|Diffraction pattern of a double slit has a single-slit [[Envelope (waves)|envelope]].]]

The notion of path difference and constructive or destructive interference used above for the double-slit experiment applies as well to the display of a single slit of light intercepted on a screen. The main result of this interference is to spread out the light from the narrow slit into a broader image on the screen. This distribution of wave energy is called [[diffraction]].

Two types of diffraction are distinguished, depending upon the separation between the source and the screen: [[Fraunhofer diffraction]] or far-field diffraction at large separations and [[Fresnel diffraction]] or near-field diffraction at close separations.

In the analysis of the single slit, the non-zero width of the slit is taken into account, and each point in the aperture is taken as the source of one contribution to the beam of light (''Huygens' wavelets''). On the screen, the light arriving from each position within the slit has a different path length, albeit possibly a very small difference. Consequently, interference occurs.

In the Fraunhofer diffraction pattern sufficiently far from a single slit, within a [[small-angle approximation]], the intensity spread ''S'' is related to position ''x'' via a squared [[sinc function]]:<ref>
{{cite book
 | title = Optical scattering: measurement and analysis
 | edition = 2nd
 | author = John C. Stover
 | publisher = SPIE Press
 | year = 1995
 | isbn = 978-0-8194-1934-7
 | page = 64
 | url = https://books.google.com/books?id=ot0tjJL72uUC&q=single-slit+diffraction+sinc-function&pg=PA65
 }}</ref>
<math display="block">S(u) = \mathrm{sinc}^2(u) = \left( \frac {\sin \pi u}{\pi u} \right) ^2 \ ; </math>
with
<math display="block">u = \frac {x L}{\lambda R} \ , </math>
where ''L'' is the slit width, ''R'' is the distance of the pattern (on the screen) from the slit, and λ is the wavelength of light used. The function ''S'' has zeros where ''u'' is a non-zero integer, where are at ''x'' values at a separation proportion to wavelength.