This article summarizes equations used in optics, including geometric optics, physical optics, radiometry, diffraction, and interferometry.
Quantity (common name/s) | (Common) symbol/s | SI units | Dimension |
---|---|---|---|
Object distance | x, s, d, u,x1, s1, d1, u1 | m | [L] |
Image distance | x', s', d', v,x2, s2, d2, v2 | m | [L] |
Object height | y, h,y1, h1 | m | [L] |
Image height | y', h', H,y2, h2, H2 | m | [L] |
Angle subtended by object | θ, θo,θ1 | rad | dimensionless |
Angle subtended by image | θ', θi,θ2 | rad | dimensionless |
Curvature radius of lens/mirror | r, R | m | [L] |
Focal length | f | m | [L] |
Quantity (common name/s) | (Common) symbol/s | Defining equation | SI units | Dimension |
---|---|---|---|---|
Lens power | P | m−1 = D (dioptre) | [L]−1 | |
Lateral magnification | m | dimensionless | dimensionless | |
Angular magnification | m | dimensionless | dimensionless | |
There are different forms of the Poynting vector, the most common are in terms of the E and B or E and H fields.
Quantity (common name/s) | (Common) symbol/s | Defining equation | SI units | Dimension |
---|---|---|---|---|
Poynting vector | S, N | W m−2 | [M][T]−3 | |
Poynting flux, EM field power flow | ΦS, ΦN | W | [M][L]2[T]−3 | |
RMS Electric field of Light | Erms | N C−1 = V m−1 | [M][L][T]−3[I]−1 | |
Radiation momentum | p, pEM, pr | J s m−1 | [M][L][T]−1 | |
Radiation pressure | Pr, pr, PEM | W m−2 | [M][T]−3 | |
For spectral quantities two definitions are in use to refer to the same quantity, in terms of frequency or wavelength.
Quantity (common name/s) | (Common) symbol/s | Defining equation | SI units | Dimension |
---|---|---|---|---|
Radiant energy | Q, E, Qe, Ee | J | [M][L]2[T]−2 | |
Radiant exposure | He | J m−2 | [M][T]−3 | |
Radiant energy density | ωe | J m−3 | [M][L]−3 | |
Radiant flux, radiant power | Φ, Φe | W | [M][L]2[T]−3 | |
Radiant intensity | I, Ie | W sr−1 | [M][L]2[T]−3 | |
Radiance, intensity | L, Le | W sr−1 m−2 | [M][T]−3 | |
Irradiance | E, I, Ee, Ie | W m−2 | [M][T]−3 | |
Radiant exitance, radiant emittance | M, Me | W m−2 | [M][T]−3 | |
Radiosity | J, Jν, Je, Jeν | W m−2 | [M][T]−3 | |
Spectral radiant flux, spectral radiant power | Φλ, Φν, Φeλ, Φeν | W m−1 (Φλ) W Hz−1 = J (Φν) | [M][L]−3[T]−3 (Φλ) [M][L]−2[T]−2 (Φν) | |
Spectral radiant intensity | Iλ, Iν, Ieλ, Ieν | W sr−1 m−1 (Iλ) W sr−1 Hz−1 (Iν) | [M][L]−3[T]−3 (Iλ) [M][L]2[T]−2 (Iν) | |
Spectral radiance | Lλ, Lν, Leλ, Leν | W sr−1 m−3 (Lλ) W sr−1 m−2 Hz−1 (Lν) | [M][L]−1[T]−3 (Lλ) [M][L]−2[T]−2 (Lν) | |
Spectral irradiance | Eλ, Eν, Eeλ, Eeν | W m−3 (Eλ) W m−2 Hz−1 (Eν) | [M][L]−1[T]−3 (Eλ) [M][L]−2[T]−2 (Eν) | |
Physical situation | Nomenclature | Equations |
---|---|---|
Energy density in an EM wave | = mean energy density | For a dielectric: |
Kinetic and potential momenta (non-standard terms in use) | Potential momentum: Kinetic momentum: Canonical momentum: | |
Irradiance, light intensity |
| At a spherical surface: |
Doppler effect for light (relativistic) | ||
Cherenkov radiation, cone angle |
| |
Electric and magnetic amplitudes |
| For a dielectric |
EM wave components | Electric Magnetic | |
Physical situation | Nomenclature | Equations |
---|---|---|
Critical angle (optics) |
| |
Thin lens equation |
| Lens focal length from refraction indices |
Image distance in a plane mirror | ||
Spherical mirror | r = curvature radius of mirror | Spherical mirror equation Image distance in a spherical mirror |
Subscripts 1 and 2 refer to initial and final optical media respectively.
These ratios are sometimes also used, following simply from other definitions of refractive index, wave phase velocity, and the luminal speed equation:
where:
Physical situation | Nomenclature | Equations |
---|---|---|
Angle of total polarisation | θB = Reflective polarization angle, Brewster's angle | |
intensity from polarized light, Malus's law |
| |
Property or effect | Nomenclature | Equation |
---|---|---|
Thin film in air |
|
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The grating equation |
| |
Rayleigh's criterion | ||
Bragg's law (solid state diffraction) |
|
where |
Single slit diffraction intensity |
| |
N-slit diffraction (N ≥ 2) |
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N-slit diffraction (all N) | ||
Circular aperture intensity |
| |
Amplitude for a general planar aperture | Cartesian and spherical polar coordinates are used, xy plane contains aperture
| Near-field (Fresnel) Far-field (Fraunhofer) |
Huygens–Fresnel–Kirchhoff principle |
| |
Kirchhoff's diffraction formula | ||
In astrophysics, L is used for luminosity (energy per unit time, equivalent to power) and F is used for energy flux (energy per unit time per unit area, equivalent to intensity in terms of area, not solid angle). They are not new quantities, simply different names.
Quantity (common name/s) | (Common) symbol/s | Defining equation | SI units | Dimension |
---|---|---|---|---|
Comoving transverse distance | DM | pc (parsecs) | [L] | |
Luminosity distance | DL | pc (parsecs) | [L] | |
Apparent magnitude in band j (UV, visible and IR parts of EM spectrum) (Bolometric) | m | dimensionless | dimensionless | |
Absolute magnitude (Bolometric) | M | dimensionless | dimensionless | |
Distance modulus | μ | dimensionless | dimensionless | |
Colour indices | (No standard symbols) | dimensionless | dimensionless | |
Bolometric correction | Cbol (No standard symbol) | dimensionless | dimensionless | |
The Fresnel equations describe the reflection and transmission of light when incident on an interface between different optical media. They were deduced by French engineer and physicist Augustin-Jean Fresnel who was the first to understand that light is a transverse wave, when no one realized that the waves were electric and magnetic fields. For the first time, polarization could be understood quantitatively, as Fresnel's equations correctly predicted the differing behaviour of waves of the s and p polarizations incident upon a material interface.
In optics, the refractive index of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.
An electric field is the physical field that surrounds electrically charged particles. Charged particles exert attractive forces on each other when their charges are opposite, and repulsion forces on each other when their charges are the same. Because these forces are exerted mutually, 2 charges must be present for the forces to take place. The electric field of a single charge describes their capacity to exert such forces on another charged object. These forces are described by Coulomb's Law, which says that the greater the magnitude of the charges, the greater the force, and the greater the distance between them, the weaker the force. Thus, we may informally say that the greater the charge of an object, the stronger its electric field. Similarly, the electric field is stronger nearer charged objects and weaker further away. Electric fields originate from electric charges and time-varying electric currents. Electric fields and magnetic fields are both manifestations of the electromagnetic field, one of the four fundamental forces of nature.
In the physical sciences, the wavenumber, also known as repetency, is the spatial frequency of a wave, measured in cycles per unit distance or radians per unit distance. It is analogous to temporal frequency, which is defined as the number of wave cycles per unit time or radians per unit time.
Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets, satellites, and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and the law of universal gravitation. Orbital mechanics is a core discipline within space-mission design and control.
Linear elasticity is a mathematical model of how solid objects deform and become internally stressed due to prescribed loading conditions. It is a simplification of the more general nonlinear theory of elasticity and a branch of continuum mechanics.
In physics, specifically relativistic quantum mechanics (RQM) and its applications to particle physics, relativistic wave equations predict the behavior of particles at high energies and velocities comparable to the speed of light. In the context of quantum field theory (QFT), the equations determine the dynamics of quantum fields. The solutions to the equations, universally denoted as ψ or Ψ, are referred to as "wave functions" in the context of RQM, and "fields" in the context of QFT. The equations themselves are called "wave equations" or "field equations", because they have the mathematical form of a wave equation or are generated from a Lagrangian density and the field-theoretic Euler–Lagrange equations.
In physics and engineering, a constitutive equation or constitutive relation is a relation between two physical quantities that is specific to a material or substance, and approximates the response of that material to external stimuli, usually as applied fields or forces. They are combined with other equations governing physical laws to solve physical problems; for example in fluid mechanics the flow of a fluid in a pipe, in solid state physics the response of a crystal to an electric field, or in structural analysis, the connection between applied stresses or loads to strains or deformations.
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In differential geometry, a tensor density or relative tensor is a generalization of the tensor field concept. A tensor density transforms as a tensor field when passing from one coordinate system to another, except that it is additionally multiplied or weighted by a power W of the Jacobian determinant of the coordinate transition function or its absolute value. A tensor density with a single index is called a vector density. A distinction is made among (authentic) tensor densities, pseudotensor densities, even tensor densities and odd tensor densities. Sometimes tensor densities with a negative weight W are called tensor capacity. A tensor density can also be regarded as a section of the tensor product of a tensor bundle with a density bundle.
In quantum mechanics, the momentum operator is the operator associated with the linear momentum. The momentum operator is, in the position representation, an example of a differential operator. For the case of one particle in one spatial dimension, the definition is:
Vacuum permittivity, commonly denoted ε0, is the value of the absolute dielectric permittivity of classical vacuum. It may also be referred to as the permittivity of free space, the electric constant, or the distributed capacitance of the vacuum. It is an ideal (baseline) physical constant. Its CODATA value is:
In physics, relativistic quantum mechanics (RQM) is any Poincaré covariant formulation of quantum mechanics (QM). This theory is applicable to massive particles propagating at all velocities up to those comparable to the speed of light c, and can accommodate massless particles. The theory has application in high energy physics, particle physics and accelerator physics, as well as atomic physics, chemistry and condensed matter physics. Non-relativistic quantum mechanics refers to the mathematical formulation of quantum mechanics applied in the context of Galilean relativity, more specifically quantizing the equations of classical mechanics by replacing dynamical variables by operators. Relativistic quantum mechanics (RQM) is quantum mechanics applied with special relativity. Although the earlier formulations, like the Schrödinger picture and Heisenberg picture were originally formulated in a non-relativistic background, a few of them also work with special relativity.
In electromagnetism, a branch of fundamental physics, the matrix representations of the Maxwell's equations are a formulation of Maxwell's equations using matrices, complex numbers, and vector calculus. These representations are for a homogeneous medium, an approximation in an inhomogeneous medium. A matrix representation for an inhomogeneous medium was presented using a pair of matrix equations. A single equation using 4 × 4 matrices is necessary and sufficient for any homogeneous medium. For an inhomogeneous medium it necessarily requires 8 × 8 matrices.