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What is a single slit

  1. Jul 24, 2014 #1
    Definition/Summary

    This entry describes diffraction of a wave when it passes through a single narrow slit.

    Equations

    The far-field (Fraunhofer) diffraction pattern has a power per area (irradiance) at an angle [itex]\theta[/itex] from a single slit of width [itex] d[/itex], for wavelength [itex]\lambda[/itex] and wavenumber [itex]k\ =\ 2\pi/\lambda[/itex] of:

    [tex]I(\theta)\ =\ \left( \frac{\sin \beta}{\beta}\right)^2\,I(0)[/tex]

    where:
    [tex]\beta\ \equiv\ \frac{\pi d}{\lambda} \ \sin\theta\ =\ \frac{k d}{2} \ \sin\theta[/tex]

    which for very small angles is approximately:
    [tex]\beta \ \approx \ \frac{\pi d}{\lambda} \ \theta \ = \ \frac{kd}{2} \ \theta[/tex]


    The diffraction minima (dark fringes) occur when

    [tex]\beta \ = \ n \pi, \ \ n \ = \ \pm 1, \ \pm 2, \ \pm 3, \ ...[/tex]

    or, for small angles,

    [tex]\theta \ \approx \ n \lambda / d, \ \ n \ = \ \pm 1, \ \pm 2, \ \pm 3, \ ...[/tex]

    Note that n=0 corresponds to the central maximum, not a minimum.

    Extended explanation

    Definition of terms
    I = irradiance of the wave, with SI units of W/m2
    I(0) = the irradiance at θ=0
    d = the slit width
    λ = the wavelength of the wave
    k = 2π/λ
    θ = the angle at which the irradiance is evaluated

    * This entry is from our old Library feature, and was originally created by Redbelly98
     
    Last edited by a moderator: Jul 27, 2014
  2. jcsd
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