Single-slit diffraction and the Heisenberg principle for position and momentum

Monochromatic light is prepared by a single slit of spatial width {\Delta}x. The diffraction pattern is considered to obtain the corresponding probability density of the momentum. Let P be the probability weight to measure a momentum in a finite window of width {\Delta}p. For small {\Delta}p the asymptotic law P ~ {\Delta}x{\Delta}p/h is verified, while h is Planck's constant of action.