Diffraction is a wave phenomenon in which propagation through an opening, past an obstacle, or through a structured material produces spreading and patterns of reinforcement and cancellation. It occurs with light, sound, surface waves, and the matter waves studied in quantum mechanics. In optics, diffraction explains why shadows are not perfectly sharp and why a finite aperture cannot form an infinitely small image of a point source. Its effects become especially conspicuous when relevant dimensions are comparable to the wavelength, although diffraction also occurs at much larger apertures. (openstax.org)
Physical basis
Diffraction is understood through interference: wave contributions arriving at an observation point combine according to their amplitudes and relative phases. Contributions in phase reinforce one another, while contributions with opposing phases can cancel. In the Huygens–Fresnel principle, points across a wavefront supply secondary wavelets whose combined effect determines the subsequent field. For an aperture, contributions from different parts of the opening travel different distances, producing a spatial distribution of intensity rather than a simple geometrical projection. (openstax.org)
“Diffraction” and “interference” therefore describe closely related aspects of wave superposition, rather than separate physical mechanisms. A single slit produces interference among contributions across its width; multiple slits introduce additional interference between openings. Sound passing through a doorway and ocean waves spreading behind a gap in a breakwater illustrate the same general behavior. (openstax.org)
Near-field and far-field diffraction
Two important approximations distinguish different observation geometries. Fresnel diffraction, commonly called near-field diffraction, retains wavefront-curvature effects. Its pattern can change substantially with distance from an opening or edge. Fraunhofer diffraction, or far-field diffraction, describes a limiting regime in which the pattern has a simpler angular structure. These are approximations to wave propagation, not different kinds of waves. (courses.washington.edu)
In the Fraunhofer regime, the diffracted field is related to the Fourier transform of the field across the aperture. Consequently, aperture shape and illumination determine the distribution of outgoing directions. The transformation applies to the complex field amplitude; the measured intensity is proportional to its squared magnitude. This relationship connects diffraction with Fourier methods used to analyze optical systems and crystalline structures. (arxiv.org)
Single slits and diffraction gratings
For monochromatic, uniform illumination normally incident on a slit of width (a), the ideal far-field intensity is
[ I(\theta)=I_0\left(\frac{\sin\beta}{\beta}\right)^2, \qquad \beta=\frac{\pi a\sin\theta}{\lambda}, ]
where (\lambda) is the wavelength, (\theta) is measured from the forward direction, and (I_0) is the central intensity. The expression approaches (I_0) at (\theta=0). Dark minima occur where
[ a\sin\theta=m\lambda, \qquad m=\pm1,\pm2,\ldots, ]
provided the corresponding angles exist. The broad central maximum is bordered by weaker secondary maxima. For small angles, its width between the first minima is approximately (2\lambda/a): narrowing the slit broadens the pattern. (openstax.org)
A diffraction grating contains many regularly spaced openings or grooves. Contributions from successive elements reinforce at selected directions; increasing the number of illuminated elements sharpens the principal maxima. Because these directions depend on wavelength, gratings separate incident light into spectral components. They are important instruments in spectroscopy, and regularly patterned natural surfaces can produce related color effects. (openstax.org)
Circular apertures and resolution
An ideal, uniformly illuminated circular aperture produces an Airy pattern: a bright central disk surrounded by weaker concentric rings. For aperture diameter (D) much larger than the wavelength, the angular radius of the first dark ring is approximately
[ \theta_1=1.22\frac{\lambda}{D}, ]
in radians. Thus, even an otherwise perfect optical instrument spreads the image of a point source over a finite region. (openstax.org)
The Rayleigh criterion conventionally treats two point-source images as just resolved when the central maximum of one falls on the first minimum of the other. For a circular aperture, it gives the angular separation above. Diffraction therefore constrains the resolution of a telescope or microscope and also causes finite-width beams to spread during propagation. Larger apertures or shorter wavelengths reduce the characteristic diffraction angle under the same assumptions. (openstax.org)
Crystals and matter waves
In crystallography, diffraction patterns arise from scattering by the ordered constituents of a crystal. Their directional reinforcement can be expressed by Bragg’s law:
[ 2d\sin\theta=n\lambda, ]
where (d) is the spacing between a family of parallel crystal planes, (\theta) is the angle between the incident beam and those planes, and (n) is a positive integer. The reciprocal lattice provides an equivalent geometrical description of diffraction conditions. (iucr.org)
In X-ray crystallography, peak directions establish geometrical information, while intensities depend on the arrangement of atoms within the unit cell. Each reflection has a structure factor specifying amplitude and phase. Reconstructing electron density requires both, but ordinary intensity measurements do not directly supply the phases; this difficulty is the phase problem. Diffraction data consequently require mathematical interpretation rather than functioning as ordinary photographs of atoms. (iucr.org)
Diffraction of the electron established experimental evidence for matter-wave behavior. Clinton Davisson and George Paget Thomson shared the 1937 Nobel Prize in Physics for discovering electron diffraction by crystals. Their experiments helped connect the wave description of matter with observable patterns of scattering. (nobelprize.org)