Diffractionsmustern

Diffractionsmustern are the spatial patterns of light or other waves that arise when waves encounter obstacles or structures with dimensions comparable to their wavelength. The observed intensity distribution results from interference among secondary wavelets emitted by the edges of apertures or by atomic or molecular planes in a crystal. In many contexts the far-field, or Fraunhofer, diffraction pattern is studied because it depends mainly on the geometry of the opening and the wavelength.

In optical experiments, simple models capture the main features of Diffractionsmustern. For a single slit of width a, the intensity follows I(θ) ∝ (sin β / β)^2 with β = π a sin θ / λ. For two slits separated by d, I(θ) ∝ cos^2(δ/2) (sin β / β)^2 with δ = 2π d sin θ / λ, producing a fringe pattern. A diffraction grating with N equally spaced slits yields sharp maxima at angles where d sin θ = m λ, and a more complex envelope I ∝ (sin Nδ/2 / sin δ/2)^2.

Beyond optics, diffraction patterns are essential in crystallography and materials science. X-ray and electron Diffractionsmustern reveal lattice spacings and crystal structures, using Bragg’s law n λ = 2 d sin θ, where d is the spacing between lattice planes. The pattern’s characteristics inform on symmetry, spacing, and arrangement of atoms.

Historically, the phenomenon was pivotal in establishing wave nature of light, with early work by Young, and later developments by Laue and Bragg that founded modern diffraction techniques used for structure determination and materials analysis.