Interference of light

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  • Width of a fringe: $$\Delta x = \frac{l}{d} \lambda,$$where $l$ is the distance from the sources to the screen, $d$ is the distance between the sources.
  • Temporal and spatial coherences. Coherence length and coherence radius: $$l_{coh}\simeq \frac{\lambda ^2}{\Delta \lambda}, \rho_{coh} \simeq \frac{\lambda}{\psi},$$where $\psi$ is the angular dimension of the source.
  • Condition for interference maxima in the case of light reflected from a thin plate of thickness $b$: $$2b \sqrt{n^2-\sin^2 \theta_1} = (k+1/2)\lambda,$$where $k$ is an integer.
  • Newton's ring produced on reflection of light from the surfaces of an air interlayer formed between a lens of radius $R$ and a glass plate with which the convex surface of the lens is in contact. The radii of the rings: $$ r = \sqrt{\lambda Rk/2},$$with the rings being bright if $k = 1, 3, 5, ...$, and dark if $k = 2, 4, 6, ...$. The value $k = 0$ corresponds to the middle of the central dark spot.

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