page_title: Wavelength
section_title: Single-slit diffraction
hierarchical_section_title: Wavelength / Interference and diffraction / Single-slit diffraction
caption_attribution_description: English: Double-slit diffraction pattern
context_page_description: In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, troughs, or zero crossings, and is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns. The inverse of the wavelength is called the spatial frequency. Wavelength is commonly designated by the Greek letter lambda.
  The term wavelength is also sometimes applied to modulated waves, and to the sinusoidal envelopes of modulated waves or waves formed by interference of several sinusoids.
  Assuming a sinusoidal wave moving at a fixed wave speed, wavelength is inversely proportional to frequency of the wave: waves with higher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths.
  Wavelength depends on the medium that a wave travels through. Examples of waves are sound waves, light, water waves and periodic electrical signals in a conductor.
context_section_description: 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 (Huygen's 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:
    with  
  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.
caption: Diffraction pattern of a double slit has a single-slit envelope.
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