concept

diffraction

Diffraction is the bending or spreading of waves, such as light or sound, around obstacles or through apertures.
14 related articles · 6 formulas · 2 who worked here

Description

Diffraction is the deviation of waves (light, sound, water) from straight-line propagation when encountering an obstacle or opening. It becomes noticeable when the slit size is comparable to the wavelength. In the case of light, it produces an interference pattern — a set of bands of varying brightness.

History

The first systematic description of light diffraction was given by the Italian physicist Francesco Grimaldi in a posthumous work of 1665, introducing the term itself. The wave nature of light, capable of explaining diffraction, was championed by Christiaan Huygens (1690). In 1801, Thomas Young demonstrated interference from two slits, confirming the wave theory. Augustin-Jean Fresnel in 1818 presented a rigorous mathematical theory, solving the problem of diffraction at an edge. Later, in 1912, Max von Laue and colleagues discovered X-ray diffraction in crystals, which earned him the Nobel Prize. William Lawrence Bragg and his father William Henry Bragg developed a method for deciphering crystal structures from diffraction patterns. Joseph von Fraunhofer invented the diffraction grating and used it for spectroscopy.

How it works

Diffraction is a consequence of wave superposition. When part of the wavefront is blocked by an obstacle, secondary waves from the open areas interfere, creating a complex pattern. For periodic structures such as a diffraction grating or crystal lattice, the condition for reinforcement is described by Bragg's law: nλ = 2d sin θ, where n is the diffraction order, λ is the wavelength, d is the interplanar spacing, and θ is the grazing angle. This law underlies X-ray crystallography. For gratings with many grooves, the intensity is concentrated in narrow peaks, allowing diffraction to be used in spectrometers to measure wavelengths with high precision.

In practice

Thanks to diffraction, spectrometer gratings work, splitting light into colors for analyzing the chemical composition of stars.

Fun fact

If you look through a thin fabric at a street lamp, you can see rainbow streaks — that's also diffraction on the threads.

Concept graph →

Formulas

$$\omega(\mathbf{k}) \neq \omega(-\mathbf{k})$$
Wave frequency depends on direction, breaking reciprocity.
What is in the formula
\omegavariableangular frequency — angular frequency radian per second
\mathbf{k}variablewave vector — wave vector radian per metre
ω({k})\neqω(-{k}) · 2606.04341
$$\mathbf{F} = -\frac{c}{\kappa \rho} \nabla e_{\text{rad}}$$
Radiation flux in diffusion approximation.
What is in the formula
\mathbf{F}variableRadiation flux vector — radiation flux watt per square metre
\kappavariableOpacity (mass absorption coefficient) — opacity square metre per kilogram
\rhovariableMass density — mass density kilogram per cubic metre
e_{\text{rad}}variableRadiation energy density — energy density joule per cubic metre
cconstantSpeed of light in vacuum — speed of light = 299792458 metre per second
\nablaoperatorSpatial gradient — nabla operator
{f}_{{diff}}=-λ\frac{c}{\kappa_s}\frac{\nablae_{{rad}}}{ρ} · 2607.05508v1
$$r_d = \sqrt{2 D t}$$
Characteristic distance particles diffuse in time t.
What is in the formula
r_dvariableDiffusion length scale — diffusion length metre
DvariableDiffusion coefficient — diffusion coefficient metre squared per second
tvariableTime elapsed — time second
r_d=\sqrt{4d(e)t} · 2607.07100
$$\theta \approx 1.22 \frac{\lambda}{D}$$
Angular resolution limit of a circular aperture.
What is in the formula
θvariableangular resolution — angular resolution radian
λvariablewavelength of light — wavelength metre
Dvariableaperture diameter — diameter metre
1.22constantFirst zero of the Airy disk for a circular aperture — airy disk constant = 1.22
θ_{{div}}\simeq2*1.22\frac{λ}{d} · 2607.12106
$$F = \frac{a^2}{\lambda L}$$
Measures diffraction regime in wave propagation.
What is in the formula
FvariableFresnel number, dimensionless diffraction parameter — fresnel number
avariableCharacteristic transverse size of aperture or obstacle — length metre
λvariableWavelength of the wave — wavelength metre
LvariablePropagation distance from aperture to observation plane — length metre
f=\frac{a^2}{λl} · 2607.13417
$$\lambda = \frac{c}{f}$$
Wavelength equals speed divided by frequency.
What is in the formula
λvariableWavelength of the wave — wavelength metre
cvariableSpeed of light in the medium — speed of light metre per second
fvariableFrequency of the wave — frequency hertz
λ=\frac{c}{f} · 2607.13535

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