diffraction

Diffraction is the bending and spreading of waves around obstacles or through apertures, resulting in interference patterns. It is a universal wave phenomenon that affects light, sound, water waves, and matter waves such as electrons. The phenomenon was studied in the early 19th century, notably by Fresnel and Young, with the term “diffraction” attributed to Fraunhofer in the context of optical experiments.

The explanation of diffraction relies on the Huygens–Fresnel principle: every point on a wavefront can be treated as a secondary source of spherical wavelets. The superposition of these wavelets determines the wave field beyond the obstacle or aperture. This framework accounts for how wavefronts bend around edges and how interference creates bright and dark regions.

Common cases include Fraunhofer (far-field) diffraction, observed when detectors are far away or when lenses create effectively parallel wavefronts, and Fresnel (near-field) diffraction, where geometry is more complex. Edge diffraction refers to bending around a sharp boundary. Characteristic patterns arise from different geometries: single-slit diffraction produces a central maximum with diminishing side lobes; double-slit interference yields a series of fringes modulated by the single-slit envelope; diffraction gratings produce multiple, sharply defined maxima.

Mathematically, a simple single-slit intensity pattern is I(θ) ∝ (sin β / β)² with β = π a sin θ / λ, where a is the slit width and λ the wavelength. For a grating with line separation d, constructive interference occurs when mλ = d sin θ.

Applications span optics and spectroscopy, imaging, astronomy, X-ray crystallography, and electron diffraction in materials science, illustrating diffraction’s role in both analytical methods and the understanding of wave behavior across disciplines.