Part of OP-02 — Wave Optics

YDSE Fringe Positions and Fringe Width

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Fringe width (distance between consecutive bright or dark fringes): β=λDd[L],SI unit: m\beta = \frac{\lambda D}{d} \quad [\text{L}], \quad \text{SI unit: m}

Bright fringe positions (from center): ynbright=nβ=nλDd,n=0,±1,±2,y_n^\text{bright} = n\beta = \frac{n\lambda D}{d}, \quad n = 0, \pm1, \pm2, \ldots

Dark fringe positions (from center): yndark=(n12)β=(2n1)λD2d,n=1,2,3,y_n^\text{dark} = \left(n - \frac{1}{2}\right)\beta = \frac{(2n-1)\lambda D}{2d}, \quad n = 1, 2, 3, \ldots

Effect of changing parameters:

ChangeEffect on β\beta
λ\lambda doubledβ\beta doubles
DD doubledβ\beta doubles
dd doubledβ\beta halved
Immersed in liquid (nn)β\beta reduced by factor nn (λ=λ/n\lambda' = \lambda/n)
DD doubled AND dd halvedβ\beta becomes 4×4\times

Pattern with white light:

  • Central fringe: white (all λ\lambda's have Δ=0\Delta = 0)
  • Higher-order fringes: colored (violet innermost, red outermost)
  • After a few orders: colors overlap → pattern unrecognizable

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