Part of OP-02 — Wave Optics

Single Slit Diffraction

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Setup: Monochromatic light passes through a single slit of width aa. On a screen at distance DD, a diffraction pattern forms.

Central maximum: At θ=0\theta = 0; brightest and widest feature.

  • Linear width: W=2λD/aW = 2\lambda D/a
  • Angular full-width: 2λ/a2\lambda/a

Minima (dark fringes): asinθ=nλa\sin\theta = n\lambda, n=1,2,3,n = 1, 2, 3, \ldots

Secondary maxima: asinθ(2n+1)λ/2a\sin\theta \approx (2n+1)\lambda/2, n=1,2,n = 1, 2, \ldots

  • Each secondary maximum width: λD/a\lambda D/a (half the central maximum width)
  • Intensities: 1st 4.5%\approx 4.5\%, 2nd 1.6%\approx 1.6\% of central maximum

YDSE vs. Single Slit Comparison:

FeatureYDSESingle Slit
Parameterdd (slit separation)aa (slit width)
Central fringeBright, uniform widthBright, twice as wide
All maximaEqual intensityRapidly decreasing
Minimum conditionΔ=(2n1)λ/2\Delta = (2n-1)\lambda/2asinθ=nλa\sin\theta = n\lambda

Important NEET trick: In single slit, the condition asinθ=nλa\sin\theta = n\lambda gives minima, NOT maxima. Opposite of YDSE!

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