For two identical slits (each intensity I0):
I=4I0cos2(2ϕ)
- Imax=4I0 at ϕ=0,2π,4π,… (constructive, path diff = $0, \lambda, 2\lambda, \ldots$)
- Imin=0 at ϕ=π,3π,5π,… (destructive, path diff = λ/2,3λ/2,…)
Energy conservation: Average intensity ⟨I⟩=2I0=I1+I2. Interference does not create or destroy energy — it redistributes it.
Fringe visibility:
V=Imax+IminImax−Imin=1(identical slits, perfect contrast)
For unequal slits (I1=I2): V<1; for completely blocked slit: V=0.
Key intensity values:
| Path difference Δ | Phase diff ϕ | I/Imax |
|---|
| $0$ | $0$ | $1$ |
| λ/6 | π/3 | $3/4$ |
| λ/4 | π/2 | $1/2$ |
| λ/3 | $2\pi/3$ | $1/4$ |
| λ/2 | π | $0$ |