Part of OP-02 — Wave Optics

Intensity Distribution in YDSE

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For two identical slits (each intensity I0I_0): I=4I0cos2 ⁣(ϕ2)I = 4I_0\cos^2\!\left(\frac{\phi}{2}\right)

  • Imax=4I0I_\text{max} = 4I_0 at ϕ=0,2π,4π,\phi = 0, 2\pi, 4\pi, \ldots (constructive, path diff = 0,λ,2λ,0, \lambda, 2\lambda, \ldots)
  • Imin=0I_\text{min} = 0 at ϕ=π,3π,5π,\phi = \pi, 3\pi, 5\pi, \ldots (destructive, path diff = λ/2,3λ/2,\lambda/2, 3\lambda/2, \ldots)

Energy conservation: Average intensity I=2I0=I1+I2\langle I \rangle = 2I_0 = I_1 + I_2. Interference does not create or destroy energy — it redistributes it.

Fringe visibility: V=ImaxIminImax+Imin=1(identical slits, perfect contrast)V = \frac{I_\text{max} - I_\text{min}}{I_\text{max} + I_\text{min}} = 1 \quad \text{(identical slits, perfect contrast)}

For unequal slits (I1I2I_1 \neq I_2): V<1V < 1; for completely blocked slit: V=0V = 0.

Key intensity values:

Path difference Δ\DeltaPhase diff ϕ\phiI/ImaxI/I_\text{max}
000011
λ/6\lambda/6π/3\pi/33/43/4
λ/4\lambda/4π/2\pi/21/21/2
λ/3\lambda/32π/32\pi/31/41/4
λ/2\lambda/2π\pi00

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