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InformationFinite graphs and trees

Graphs represent pairwise connections; trees impose acyclicity.

DefinitionInformationData-structure interfaces and operation costs

An interface defines operations; an implementation determines costs.

MethodInformationLoop invariants and total correctness

An invariant establishes correctness only with its proof obligations.

MethodInformationComparison sorting lower bound

Distinct-key comparisons need enough branches to distinguish orders.

Mathematical statementInformationBreadth-first and depth-first traversal

Graph searches visit reachable vertices using different orders.

MethodInformationShortest-path algorithm conditions

Edge weights determine which shortest-path method applies.

MethodInformationTuring machines and effective computation

Finite instructions can act on an unbounded writable tape.

DefinitionInformationRelations and tabular data

A relation is a set of tuples from declared domains.

DefinitionPhysicsCentre-of-mass dynamics

External force controls the mass-weighted centre's acceleration.

ModelPhysicsRigid-body inertia tensor

A tensor relates rotation to angular momentum.

ModelPhysicsEuler equations for a rigid body

Body-axis angular acceleration includes rotation of the axes.

ModelPhysics · Mathematics & logicEuler–Lagrange equations

Stationary action supplies coordinate equations of motion.

Mathematical statementPhysics · Mathematics & logicHamilton's canonical equations

Canonical coordinates and momenta evolve from the Hamiltonian.

Mathematical statementPhysicsFluid mass continuity

Density change balances mass flux through a region.

ModelPhysicsBernoulli's streamline relation

An ideal steady flow balances pressure, motion and height.

ModelPhysicsIncompressible Navier–Stokes equation

Fluid inertia balances pressure, viscosity and gravity.

ModelPhysicsReynolds number

Compare inertial and viscous scales of a flow.

ModelPhysicsDriven damped oscillator

A linear restoring force, damping and periodic drive determine response.

ModelPhysicsIdeal-string wave equation

A local differential equation determines small string disturbances.

ModelPhysics · Mathematics & logicWave superposition and interference

Linear disturbances add; their relative phase determines reinforcement.

ModelPhysicsFixed-end string modes

Boundary conditions select standing-wave frequencies.

ModelPhysicsSnell's refraction relation

Angles at an interface depend on refractive indices.

ModelPhysicsThin-lens image equation

A paraxial lens relates object and image distances.

ModelPhysicsSingle-slit diffraction minima

An aperture's finite width selects dark far-field directions.

ModelPhysicsLinear polarization and Malus's law

An ideal analyzer transmits the field component along its axis.

ModelPhysicsElectromagnetic potentials

Scalar and vector potentials encode electric and magnetic fields.

ModelPhysicsCapacitance

A linear two-conductor arrangement stores separated charge.

DefinitionPhysicsSelf-inductance

Changing current changes linked magnetic flux and induced emf.

ModelPhysicsElectromagnetic energy balance

The rate of field-energy change balances outward energy flow and power transferred to charges.

ModelPhysicsKirchhoff circuit balances

Lumped circuit models balance node currents and loop voltages.

Model
ModelSource checked

Single-slit diffraction minima

Physics

An aperture's finite width selects dark far-field directions.

Key knowledge

For uniform monochromatic illumination of a single slit, Fraunhofer diffraction minima occur at a sin θ = mλ for nonzero integers m within the allowed angular range.

Values and equations

a sin θ = mλ, m = ±1,±2,…

a
Slit width m
λ
Light wavelength in the propagation medium m
θ
Angle from the forward direction rad
m
Nonzero integer diffraction order

Conditions and scope

  • Far-field approximation, or a lens forming the far-field pattern; slit width a > 0 and normal plane-wave illumination with uniform phase and amplitude across the slit.
  • m = 0 is the central maximum, not a dark fringe; finite near-field patterns need another model.
Sources · 1

References

Sources retain their recorded scope. A source link alone does not establish verification of every statement.

  1. University Physics 3: Single-Slit DiffractionSamuel J. Ling, Jeff Sanny and William Moebs / OpenStax, Rice UniversityTextbook chapteropenstax.orgRead source

Evidence and review

Section 4.1: paired-wave cancellation and nonzero-order minima.

2026-10-10 · Uniform single-slit far-field minima only; multi-aperture or vector diffraction excluded.

Related reference entries

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Scientific relationships · 2 / 2

The relationship type describes the connection. Its linked statements, sources and conditions define the scope.

  1. Related to
    Relationship sources · 1

    Linked statements

    • For uniform monochromatic illumination of a single slit, Fraunhofer diffraction minima occur at a sin θ = mλ for nonzero integers m within the allowed angular range.

    Uniform-phase aperture contributions cancel at the stated nonzero far-field minima.

  2. Related to
    Relationship sources · 2

    Linked statements

    • A circular aperture has a diffraction angular scale proportional to wavelength divided by diameter. Atmospheric turbulence can broaden a ground-based image beyond this scale; adaptive optics corrects measured wavefront distortions within its operating limits. Collecting more photons and resolving closer objects are distinct capabilities.

    Wave diffraction constrains the aperture's image.

Entry detailsPermanent link to this entry ↗
Record identity
physics-diffraction
Revision
university-reference.1
Structured reference record
University reference · University core expansion