Fraunhofer diffraction from a single slit

The phenomenon of diffraction

Diffraction is the deviation from the straight-line propagation of light when it encounters an obstacle or an aperture of a size comparable to the wavelength. The Huygens–Fresnel principle models each point of an open slit as a secondary point source; the observed pattern results from the interference of all these sources.

Diffraction through a single slit (Fraunhofer)

For a slit of width a illuminated by a plane wave and observed at a great distance (or in the focal plane of a converging lens), the diffracted intensity in the direction θ is given by:

I(theta) = I0 * (sin(u)/u)^2, where u = piasin(theta)/lambda

The intensity minima (zeroes) are given by:

asin(theta) = klambda, where k is a non-zero integer

The central spot, between the first two minima (k = +1 and k = -1), concentrates the bulk of the light energy and has a total angular width of 2*lambda/a.

Common pitfall

Do not confuse the condition for a minimum in single-slit diffraction (asin(theta) = klambda, where k is non-zero) with the condition for a maximum in double-slit interference (delta = k*lambda, including k = 0). These are two distinct physical phenomena, even though the formulae are similar: the narrower the slit (the smaller a), the more pronounced the diffraction (wide central spot); conversely, the larger a is compared to λ, the more negligible the diffraction becomes and the propagation returns to being almost rectilinear.