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This article summarizes [[equation]]s in the theory of [[photonics]], including [[geometric optics]], [[physical optics]], [[radiometry]], [[diffraction]], and [[interferometry]].<!--maybe include [[photmetry]] later-->

==Definitions==

===Geometric optics (luminal rays)===

{{Main|Geometrical optics}}

====General fundamental quantities====

:{| class="wikitable"
|-
! scope="col" width="100" | Quantity (common name/s) 
! scope="col" width="100" | (Common) symbol/s 
! scope="col" width="125" | SI units 
! scope="col" width="100" | Dimension
|-
! Object distance
| ''x, s, d, u,'' ''x''<sub>1</sub>, ''s''<sub>1</sub>, ''d''<sub>1</sub>, ''u''<sub>1</sub>
| m
| [L]
|-
! Image distance
| ''x', s', d', v,'' ''x''<sub>2</sub>, ''s''<sub>2</sub>, ''d''<sub>2</sub>, ''v''<sub>2</sub>
| m
| [L]
|-
! Object height
| ''y, h,'' ''y''<sub>1</sub>, ''h''<sub>1</sub>
| m
| [L]
|-
! Image height
| ''y', h', H,'' ''y''<sub>2</sub>, ''h''<sub>2</sub>, ''H''<sub>2</sub>
| m
| [L]
|-
! Angle subtended by object
| ''θ, θ<sub>o</sub>,'' ''θ''<sub>1</sub>
| rad
| dimensionless
|-
! Angle subtended by image
| ''θ', θ<sub>i</sub>,'' ''θ''<sub>2</sub>
| rad
| dimensionless
|-
! Curvature radius of lens/mirror
| ''r, R''
| m
| [L]
|-
! Focal length
| ''f''
| m
| [L]
|-
|}

:{| class="wikitable"
|-
! scope="col" width="100" | Quantity (common name/s) 
! scope="col" width="100" | (Common) symbol/s 
! scope="col" width="300" | Defining equation 
! scope="col" width="125" | SI units 
! scope="col" width="100" | Dimension
|-
! Lens power
| ''P''
| <math>P = 1/f \,\!</math>
| m<sup>−1</sup> = D (dioptre)
| [L]<sup>−1</sup>
|-
! Lateral magnification
| ''m''
| <math>m = - x_2/x_1 = y_2/y_1 \,\!</math>
| dimensionless
| dimensionless
|-
! Angular magnification
| ''m''
| <math>m = \theta_2/\theta_1 \,\!</math>
| dimensionless
| dimensionless
|-
|}

===Physical optics (EM luminal waves)===

{{Main|Physical optics}}

There are different forms of the [[Poynting vector]], the most common are in terms of the '''E''' and '''B''' or '''E''' and '''H''' fields.

:{| class="wikitable"
|-
! scope="col" width="100" | Quantity (common name/s) 
! scope="col" width="100" | (Common) symbol/s 
! scope="col" width="300" | Defining equation 
! scope="col" width="125" | SI units 
! scope="col" width="100" | Dimension
|-
![[Poynting vector]]
| '''S''', '''N'''
|<math>\mathbf{N} = \frac{1}{\mu_0}\mathbf{E}\times\mathbf{B} = \mathbf{E}\times\mathbf{H} \,\!</math>
| W m<sup>&minus;2</sup>
| [M][T]<sup>&minus;3</sup>
|-
!Poynting flux, EM field power flow
| ''Φ<sub>S</sub>'', ''Φ<sub>N</sub>''
|<math> \Phi_N = \int_S \mathbf{N} \cdot \mathrm{d}\mathbf{S} \,\!</math>
| W 
| [M][L]<sup>2</sup>[T]<sup>&minus;3</sup>
|-
![[Root mean square|RMS]] [[Electric field]] of Light
| ''E''<sub>rms</sub>
|<math>E_\mathrm{rms} = \sqrt{\langle E^2 \rangle} = E/\sqrt{2}\,\!</math>
| N C<sup>&minus;1</sup> = V m<sup>&minus;1</sup>
| [M][L][T]<sup>&minus;3</sup>[I]<sup>&minus;1</sup>
|-
!Radiation momentum 
| ''p, p<sub>EM</sub>, p<sub>r</sub>''
|<math> p_{EM} = U/c\,\!</math>
| J s m<sup>&minus;1</sup> 
| [M][L][T]<sup>&minus;1</sup>
|-
![[Radiation pressure]] 
| ''P<sub>r</sub>, p<sub>r</sub>, P<sub>EM</sub>''
|<math>P_{EM} = I/c = p_{EM}/At \,\!</math>
| W m<sup>&minus;2</sup>
| [M][T]<sup>&minus;3</sup>
|-
|}

===Radiometry===

{{Main|Radiometry}}

[[File:Flux and solid angle.svg|right|275px|''275px''|thumb|Visulization of flux through differential area and solid angle. As always <math> \mathbf{\hat{n}} \,\!</math> is the unit normal to the incidant surface A, <math> \mathrm{d} \mathbf{A} = \mathbf{\hat{n}}\mathrm{d}A \,\!</math>, and <math> \mathbf{\hat{e}}_{\angle} \,\!</math> is a unit vector in the direction of incident flux on the area element, ''θ'' is the angle between them. The factor <math> \mathbf{\hat{n}} \cdot \mathbf{\hat{e}}_{\angle} \mathrm{d}A = \mathbf{\hat{e}}_{\angle} \cdot \mathrm{d}\mathbf{A} = \cos \theta \mathrm{d}A \,\!</math> arises when the flux is not normal to the surface element, so the area normal to the flux is reduced.]]

For spectral quantities two definitions are in use to refer to the same quantity, in terms of frequency or wavelength. 

:{| class="wikitable"
|-
! scope="col" width="100" | Quantity (common name/s) 
! scope="col" width="100" | (Common) symbol/s 
! scope="col" width="300" | Defining equation 
! scope="col" width="125" | SI units 
! scope="col" width="100" | Dimension
|-
! [[Radiant energy]]
| ''Q, E, Q<sub>e</sub>, E<sub>e</sub>''
| 
| J
| [M][L]<sup>2</sup>[T]<sup>&minus;2</sup>
|-
! [[Radiant exposure]] 
| ''H<sub>e</sub>''
| <math> H_e = \mathrm{d} Q/\left ( \mathbf{\hat{e}}_{\angle} \cdot \mathrm{d}\mathbf{A} \right ) \,\!</math>
| J m<sup>&minus;2</sup>
| [M][T]<sup>&minus;3</sup>
|-
! Radiant energy density
| ''ω<sub>e</sub>''
| <math> \omega_e = \mathrm{d} Q/\mathrm{d}V \,\!</math>
| J m<sup>&minus;3</sup>
| [M][L]<sup>&minus;3</sup>
|- 
! [[Radiant flux]], radiant power
| ''Φ, Φ<sub>e</sub>''
| <math> Q = \int \Phi \mathrm{d} t </math>
| W
| [M][L]<sup>2</sup>[T]<sup>&minus;3</sup>
|-
! [[Radiant intensity]]
| ''I, I<sub>e</sub>''
| <math> \Phi = I \mathrm{d} \Omega \,\!</math>
| W sr<sup>&minus;1</sup>
| [M][L]<sup>2</sup>[T]<sup>&minus;3</sup>
|- 
! [[Radiance]], intensity 
| ''L, L<sub>e</sub>''
| <math> \Phi = \iint L\left ( \mathbf{\hat{e}}_{\angle} \cdot \mathrm{d}\mathbf{A} \right ) \mathrm{d} \Omega</math>
| W sr<sup>&minus;1</sup> m<sup>&minus;2</sup>
| [M][T]<sup>&minus;3</sup>
|- 
! [[Irradiance]]
| ''E, I, E<sub>e</sub>, I<sub>e</sub>''
| <math> \Phi  = \int E \left ( \mathbf{\hat{e}}_{\angle} \cdot \mathrm{d}\mathbf{A} \right ) </math>
| W m<sup>&minus;2</sup>
|[M][T]<sup>&minus;3</sup>
|- 
! [[Radiant exitance]], radiant emittance
| ''M, M<sub>e</sub>''
| <math> \Phi = \int M \left ( \mathbf{\hat{e}}_{\angle} \cdot \mathrm{d}\mathbf{A} \right ) </math>
| W m<sup>&minus;2</sup>
| [M][T]<sup>&minus;3</sup>
|-  
! [[Radiosity (heat transfer)|Radiosity]]
| ''J, J<sub>ν</sub>, Je, J<sub>eν</sub>''
| <math> J = E + M \,\!</math>
| W m<sup>&minus;2</sup>
| [M][T]<sup>&minus;3</sup>
|- 
! Spectral radiant flux, spectral radiant power
| ''Φ<sub>λ</sub>, Φ<sub>ν</sub>, Φ<sub>eλ</sub>, Φ<sub>eν</sub>''
| <math> Q=\iint\Phi_\lambda{\mathrm{d} \lambda \mathrm{d} t}</math>

<math>Q = \iint \Phi_\nu  \mathrm{d} \nu \mathrm{d} t </math>
| W m<sup>&minus;1</sup> (''Φ''<sub>λ</sub>) <br /> W Hz<sup>&minus;1</sup> = J (''Φ''<sub>ν</sub>)
| [M][L]<sup>&minus;3</sup>[T]<sup>&minus;3</sup> (''Φ''<sub>λ</sub>) <br /> [M][L]<sup>&minus;2</sup>[T]<sup>&minus;2</sup> (''Φ''<sub>ν</sub>)
|- 
! Spectral radiant intensity
| ''I<sub>λ</sub>, I<sub>ν</sub>, I<sub>eλ</sub>, I<sub>eν</sub>''
| <math> \Phi = \iint I_\lambda \mathrm{d} \lambda \mathrm{d} \Omega</math>

<math>\Phi = \iint I_\nu \mathrm{d} \nu \mathrm{d} \Omega </math>
| W sr<sup>&minus;1</sup> m<sup>&minus;1</sup> (''I<sub>λ</sub>'') <br /> W sr<sup>&minus;1</sup> Hz<sup>&minus;1</sup> (''I<sub>ν</sub>'')
| [M][L]<sup>&minus;3</sup>[T]<sup>&minus;3</sup> (''I<sub>λ</sub>'')<br /> [M][L]<sup>2</sup>[T]<sup>&minus;2</sup> (''I<sub>ν</sub>'')
|- 
! [[Spectral radiance]]
| ''L<sub>λ</sub>, L<sub>ν</sub>, L<sub>eλ</sub>, L<sub>eν</sub>''
| <math> \Phi = \iiint L_\lambda \mathrm{d} \lambda \left ( \mathbf{\hat{e}}_{\angle} \cdot \mathrm{d}\mathbf{A} \right ) \mathrm{d} \Omega</math>

<math>\Phi = \iiint L_\nu \mathrm{d} \nu \left ( \mathbf{\hat{e}}_{\angle} \cdot \mathrm{d}\mathbf{A} \right ) \mathrm{d} \Omega \,\!</math> 
| W sr<sup>−1</sup> m<sup>−3</sup> (''L''<sub>λ</sub>)<br /> W sr<sup>−1</sup> m<sup>−2</sup> Hz<sup>−1</sup> (''L''<sub>ν</sub>)
| [M][L]<sup>−1</sup>[T]<sup>−3</sup> (''L''<sub>λ</sub>)<br /> [M][L]<sup>−2</sup>[T]<sup>−2</sup> (''L''<sub>ν</sub>)
|-
! [[Spectral irradiance]]
| ''E<sub>λ</sub>, E<sub>ν</sub>, E<sub>eλ</sub>, E<sub>eν</sub>''
| <math> \Phi = \iint E_\lambda \mathrm{d} \lambda \left ( \mathbf{\hat{e}}_{\angle} \cdot \mathrm{d}\mathbf{A} \right )</math>

<math>\Phi = \iint E_\nu \mathrm{d} \nu \left ( \mathbf{\hat{e}}_{\angle} \cdot \mathrm{d}\mathbf{A} \right ) </math>
| W m<sup>−3</sup> (''E''<sub>λ</sub>) <br /> W m<sup>−2</sup> Hz<sup>−1</sup> (''E''<sub>ν</sub>)
| [M][L]<sup>−1</sup>[T]<sup>−3</sup> (''E''<sub>λ</sub>) <br /> [M][L]<sup>−2</sup>[T]<sup>−2</sup> (''E''<sub>ν</sub>)
|- 
|}

==Equations==

===Luminal electromagnetic waves===

:{| class="wikitable"
|-
! scope="col" width="200" | Physical situation
! scope="col" width="200" | Nomenclature 
! scope="col" width="350" | Equations
|-
!Energy density in an EM wave
| <div class="plainlist">
*<math>\langle u \rangle \,\!</math> = mean energy density
</div>
| For a dielectric:<br />
<div class="plainlist">
*<math>\langle u \rangle = \frac{1}{2} \left ( \epsilon \mathbf{E}^2 + \mu \mathbf{B}^2 \right ) \,\!</math>
</div>
|-
![[Kinetic momentum|Kinetic and potential momenta]] (non-standard terms in use)
| 
|Potential momentum:
<math>\mathbf{p}_\mathrm{p} = q\mathbf{A} \,\!</math>

Kinetic momentum:
<math>\mathbf{p}_\mathrm{k} = m\mathbf{v} \,\!</math>

Cononical momentum:
<math>\mathbf{p} = m\mathbf{v} + q\mathbf{A} \,\!</math>
|-
![[Irradiance]], light intensity
| <div class="plainlist">
*<math> \langle \mathbf{S} \rangle \,\!</math> = [[Poynting vector#Examples and applications|time averaged poynting vector]]
*''I'' = [[irradiance]]
*''I''<sub>0</sub> = intensity of source
*''P''<sub>0</sub> = power of point source
*Ω = solid angle
*'''r''' = radial position from source
</div>
|<math>I = \langle \mathbf{S} \rangle = E^2_\mathrm{rms}/c\mu_0\,\!</math>

At a spherical surface:
<math>I = \frac{P_0}{\Omega \left | r \right |^2}\,\!</math>
|-
! Doppler effect for light (relativistic)
|
|<math>\lambda=\lambda_0\sqrt{\frac{c-v}{c+v}}\,\!</math>

<math>v=|\Delta\lambda|c/\lambda_0\,\!</math>
|-
! [[Cherenkov radiation]], cone angle
| <div class="plainlist">
*''n'' = refractive index
*''v'' = speed of particle
*''θ'' = cone angle
</div>
|<math> \cos \theta = \frac{v}{n c} = v\sqrt{\epsilon_0\mu_0} \,\!</math>
|-
!Electric and magnetic amplitudes
|<div class="plainlist">
*'''E''' = electric field
*'''H''' = magnetic field strength
</div>
|For a dielectric
<math>\left | \mathbf{E} \right | = \sqrt{\frac{\epsilon}{\mu}} \left | \mathbf{H} \right | \,\!</math>
|-
!EM wave components
|
|Electric 
<math>\mathbf{E} = \mathbf{E}_0 \sin(kx-\omega t)\,\!</math>

Magnetic

<math>\mathbf{B} = \mathbf{B}_0 \sin(kx-\omega t)\,\!</math>
|-
|}

===Geometric optics===

:{| class="wikitable"
|-
! scope="col" width="100" | Physical situation
! scope="col" width="200" | Nomenclature 
! scope="col" width="350" | Equations
|-
![[Critical angle (optics)]]
|<div class="plainlist">
*''n''<sub>1</sub> = refractive index of initial medium
*''n''<sub>2</sub> = refractive index of final medium
*''θ<sub>c</sub>'' = critical angle
</div>
|<math>\sin\theta_c = \frac{n_2}{n_1}\,\!</math>
|-
![[Thin lens]] equation
| <div class="plainlist">
*''f'' = lens focal length
*''x''<sub>1</sub> = object length
*''x''<sub>2</sub> = image length
*''r''<sub>1</sub> = incident curvature radius
*''r''<sub>2</sub> = refracted curvature radius
</div>
|<math>\frac{1}{x_1} +\frac{1}{x_2} = \frac{1}{f} \,\!</math>

[[Lens (optics)|Lens]] [[focal length]] from [[refraction]] indices<br />
<math>\frac{1}{f} = \left ( \frac{{n}_\mathrm{lens}}{n_\mathrm{med}-1} \right )\left ( \frac{1}{r_1} - \frac{1}{r_2} \right )\,\!</math>
|-
![[Image]] distance in a [[plane mirror]]
|
|<math>x_2 = -x_1\,\!</math>
|-
![[Spherical mirror]]
| <div class="plainlist">
*''r'' = curvature radius of mirror
</div>
| Spherical mirror equation
<math>\frac{1}{x_1} + \frac{1}{x_2} = \frac{1}{f}= \frac{2}{r}\,\!</math>

[[Image]] distance in a [[spherical mirror]]
<math>\frac{n_1}{x_1} + \frac{n_2}{x_2} = \frac{\left ( n_2 - n_1 \right )}{r}\,\!</math>
|-
|}

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:

<math> \frac{n_1}{n_2} = \frac{v_2}{v_1} = \frac{\lambda_2}{\lambda_1} = \sqrt{\frac{\epsilon_1 \mu_1}{\epsilon_2 \mu_2}} \,\!</math>

where:<div class="plainlist">
*''ε'' = [[permittivity]] of medium,
*''μ'' = [[Permeability (electromagnetism)|permeability]] of medium,
*''λ'' = [[wavelength]] of light in medium,
*''v'' = [[speed of light]] in media.
</div>

===Polarization===

:{| class="wikitable"
! scope="col" width="100" | Physical situation
! scope="col" width="250" | Nomenclature 
! scope="col" width="10" | Equations
|-
![[Brewster angle|Angle of total polarisation]]
| <div class="plainlist">
*''θ<sub>B</sub>'' = Reflective polarization angle, [[Brewster's angle]]
</div>
|<math>\tan \theta_B = n_2/n_1\,\!</math>
|-
![[Intensity (physics)|intensity]] from polarized light, [[Malus' law]]
| <div class="plainlist">
*''I''<sub>0</sub> = Initial intensity,
*''I'' = Transmitted intensity,
*θ = Polarization angle between [[polarizer]] transmission axes and electric field vector
</div>
|<math>I = I_0\cos^2\theta\,\!</math>
|-
|}

===Diffraction and interference===

:{| class="wikitable"
! scope="col" width="100" | Property or effect 
! scope="col" width="250" | Nomenclature
! scope="col" width="10" | Equation 
|-
![[Thin-film optics|Thin film]] in air
|<div class="plainlist">
*''n''<sub>1</sub> = refractive index of initial medium (before film interference)
*''n''<sub>2</sub> = refractive index of final medium (after film interference)
</div>
| <div class="plainlist">
*Minima: <math>N \lambda/n_2\,\!</math>
*Maxima:<math>2L = (N + 1/2)\lambda/n_2\,\!</math>
</div>
|-
!The grating equation
| <div class="plainlist">
*''a'' = width of aperture, slit width
*α = incident angle to the normal of the grating plane
</div>
|<math>\frac{\delta}{2\pi}\lambda = a \left ( \sin\theta + \sin\alpha \right ) \,\!</math>
|-
![[Rayleigh's criterion]]
|
|<math>\theta_R = 1.22\lambda/\,\!d</math>
|-
![[Bragg's law]] (solid state diffraction)
| <div class="plainlist">
* ''d'' = lattice spacing
*''δ'' = phase difference between two waves
</div>
|<math> \frac{\delta}{2\pi} \lambda = 2d \sin\theta \,\!</math>
<div class="plainlist">
*For constructive interference: <math> \delta/2\pi = n \,\!</math>
*For destructive interference: <math> \delta/2\pi = n/2 \,\!</math>
</div>

where <math> n \in \mathbf{N}\,\!</math>
|-
!Single slit diffraction intensity
| <div class="plainlist">
*''I''<sub>0</sub> = source intensity
*Wave phase through apertures
<math> \phi = \frac{2 \pi a}{\lambda} \sin\theta \,\!</math> 
</div>
| <math> I = I_0 \left [ \frac{ \sin \left( \phi/2 \right ) }{\left( \phi/2 \right )} \right ]^2 \,\!</math> <br />
|-
!''N''-slit diffraction (''N'' ≥ 2)
| <div class="plainlist">
*''d'' = centre-to-centre separation of slits
*''N'' = number of slits
*Phase between ''N'' waves emerging from each slit
<math> \delta = \frac{2 \pi d}{\lambda} \sin\theta \,\!</math>
</div>
| <math> I = I_0 \left [ \frac{ \sin \left( N \delta/2 \right ) }{\sin \left( \delta/2 \right )} \right ]^2 \,\!</math> <br />
|-
!''N''-slit diffraction (all ''N'')
|
| <math> I = I_0 \left [ \frac{ \sin \left( \phi/2 \right ) }{\left( \phi/2 \right )} \frac{ \sin \left( N \delta/2 \right ) }{\sin \left( \delta/2 \right )} \right ]^2 \,\!</math>
|-
!Circular aperture intensity
| <div class="plainlist">
*''a'' = radius of the circular aperture
*''J''<sub>1</sub> is a [[Bessel function]]
</div>
|<math>I = I_0 \left ( \frac{2 J_1(ka \sin \theta)}{ka \sin \theta} \right )^2</math>
|-
![[Diffraction#General aperture|Amplitude for a general planar aperture]]
|Cartesian and spherical polar coordinates are used, xy plane contains aperture
<div class="plainlist">
*''A'', amplitude at position '''r'''
*'''r'''' = source point in the aperture
*''E''<sub>inc</sub>, magnitude of incident electric field at aperture
</div>
| Near-field (Fresnel)
<math>A\left ( \mathbf{r} \right ) \propto \iint_\mathrm{aperture} E_\mathrm{inc} \left ( \mathbf{r}' \right )~ \frac{e^{ik \left | \mathbf{r} - \mathbf{r}' \right |}}{4 \pi \left | \mathbf{r} - \mathbf{r}' \right |} \mathrm{d}x'\mathrm{d}y'</math>

Far-field (Fraunhofer)
<math>A \left ( \mathbf{r} \right ) \propto \frac{e^{ik r}}{4 \pi r} \iint_\mathrm{aperture} E_\mathrm{inc}\left ( \mathbf{r}' \right ) e^{-ik \left [ \sin \theta \left ( \cos \phi x' + \sin \phi y' \right ) \right ] } \mathrm{d}x'\mathrm{d}y'</math>
|-
!Huygen-Fresnel-Kirchhoff principle
| <div class="plainlist">
*'''r'''<sub>0</sub> = position from source to aperture, incident on it
*'''r''' = position from aperture diffracted from it to a point
*α<sub>0</sub> = incident angle with respect to the normal, from source to aperture
*α = diffracted angle, from aperture to a point
*''S'' = imaginary surface bounded by aperture
*<math>\mathbf{\hat{n}}\,\!</math> = unit normal vector to the aperture
*<math> \mathbf{r}_0 \cdot \mathbf{\hat{n}} = \left | \mathbf{r}_0 \right | \cos \alpha_0 \,\!</math>
*<math> \mathbf{r} \cdot \mathbf{\hat{n}} = \left | \mathbf{r} \right | \cos \alpha \,\!</math>
*<math> \left | \mathbf{r} \right |\left | \mathbf{r}_0 \right | \ll \lambda \,\!</math>
</div>
|<math> A \mathbf ( \mathbf{r} ) = \frac{-i}{2\lambda} \iint_\mathrm{aperture} \frac{e^{i \mathbf{k} \cdot \left ( \mathbf{r} + \mathbf{r}_0 \right ) }}{ \left | \mathbf{r} \right |\left | \mathbf{r}_0 \right |} \left [ \cos \alpha_0  - \cos \alpha \right ] \mathrm{d}S \,\!</math>
|-
![[Kirchhoff's diffraction formula]]
|
|<math> A \left ( \mathbf{r} \right ) = - \frac{1}{4 \pi} \iint_\mathrm{aperture} \frac{e^{i \mathbf{k} \cdot \mathbf{r}_0}}{\left | \mathbf{r}_0 \right |} \left[ i \left | \mathbf{k} \right | U_0 \left ( \mathbf{r}_0 \right ) \cos{\alpha} + \frac {\partial A_0 \left ( \mathbf{r}_0 \right )}{\partial n} \right ] \mathrm{d}S </math>
|-
|}

==Astrophysics definitions==

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.

:{| class="wikitable"
|-
! scope="col" width="100" | Quantity (common name/s) 
! scope="col" width="100" | (Common) symbol/s 
! scope="col" width="300" | Defining equation 
! scope="col" width="125" | SI units 
! scope="col" width="100" | Dimension
|-
! Comoving transverse distance
| ''D<sub>M</sub>''
| 
| pc ([[parsecs]])
| [L]
|-
! [[Luminosity distance]]
| ''D<sub>L</sub>''
| <math>D_L = \sqrt{\frac{L}{4\pi F}} \,</math> 
| pc ([[parsecs]])
| [L]
|-
! [[Apparent magnitude]] in  band ''j'' (UV, visible and IR parts of [[EM spectrum]]) (Bolometric)
| ''m''
| <math>m_j= -\frac{5}{2} \log_{10} \left | \frac {F_j}{F_j^0} \right | \,</math>
| dimensionless
| dimensionless
|-
! [[Absolute magnitude]]
(Bolometric)
| ''M''
|<math> M = m - 5 \left [ \left ( \log_{10}{D_L} \right ) - 1 \right ]\!\,</math>
| dimensionless
| dimensionless
|-
! [[Distance modulus]]
| ''μ''
|<math> \mu = m - M \!\,</math>
| dimensionless
| dimensionless
|-
! [[Color index|Colour indices]]
| (No standard symbols)
|<math> U-B = M_U - M_B\!\,</math><br />
<math> B-V = M_B - M_V\!\,</math>
| dimensionless
| dimensionless
|-
! [[Bolometric correction]]
| ''C''<sub>bol</sub> (No standard symbol)
|<math> \begin{align} C_\mathrm{bol} & = m_\mathrm{bol} - V \\
& = M_\mathrm{bol} - M_V 
\end{align} \!\,</math>
| dimensionless
| dimensionless
|-
|}

==See also==

*[[Defining equation (physics)]]
*[[Defining equation (physical chemistry)]]
*[[List of equations in classical mechanics]]
*[[List of equations in wave theory]]
*[[List of relativistic equations]]
*[[List of electromagnetism equations]]
*[[List of equations in gravitation]]
*[[List of equations in quantum mechanics]]
*[[List of equations in nuclear and particle physics]]

==Footnotes==
{{Reflist}}

==Sources==
* {{cite book| author=P.M. Whelan, M.J. Hodgeson| title=Essential Principles of Physics| publisher=John Murray|edition=2nd| year=1978 | isbn=0-7195-3382-1}}
* {{cite book| author=G. Woan| title=The Cambridge Handbook of Physics Formulas| publisher=Cambridge University Press|edition=| year=2010| isbn=978-0-521-57507-2}}
* {{cite book| author=A. Halpern| title=3000 Solved Problems in Physics, Schaum Series| publisher=Mc Graw Hill|edition=| year=1988| isbn=978-0-07-025734-4}}
* {{cite book|pages=12–13| author=R.G. Lerner, G.L. Trigg| title=Encyclopaedia of Physics| publisher=VHC Publishers, Hans Warlimont, Springer|edition=2nd| year=2005| isbn=978-0-07-025734-4}}
* {{cite book|page=| author=C.B. Parker| title=McGraw Hill Encyclopaedia of Physics| publisher=McGraw Hill|edition=2nd| year=1994| isbn=0-07-051400-3}}
* {{cite book|page=| author=P.A. Tipler, G. Mosca| title=Physics for Scientists and Engineers: With Modern Physics| publisher=W.H. Freeman and Co|edition=6th| year=2008| isbn=9-781429-202657}}
* {{cite book|title=Analytical Mechanics|author=L.N. Hand, J.D. Finch|publisher=Cambridge University Press, |year=2008|isbn=978-0-521-57572-0}}
* {{cite book|title=Mechanics, Vibrations and Waves|author=T.B. Arkill, C.J. Millar|publisher=John Murray, |year=1974|isbn=0-7195-2882-8}}
* {{cite book|title=The Physics of Vibrations and Waves|edition=3rd|author=H.J. Pain|publisher=John Wiley & Sons, |year=1983|isbn=0-471-90182-2}}
* {{cite book|title=Dynamics and Relativity|author=J.R. Forshaw, A.G. Smith|publisher=Wiley, |year=2009|isbn=978-0-470-01460-8}}
* {{cite book|title=Electricity and Modern Physics |edition=2nd|author=G.A.G. Bennet|publisher=Edward Arnold (UK)|year=1974|isbn=0-7131-2459-8}}
* {{cite book|title=Electromagnetism (2nd Edition)|author=I.S. Grant, W.R. Phillips, Manchester Physics|publisher=John Wiley & Sons|year=2008|isbn=978-0-471-92712-9}}
* {{cite book|title=Introduction to Electrodynamics|edition=3rd |author=D.J. Griffiths|publisher=Pearson Education, Dorling Kindersley, |year=2007|isbn=81-7758-293-3}}

==Further reading==
* {{cite book|title=Physics with Modern Applications|author=L.H. Greenberg|publisher=Holt-Saunders International W.B. Saunders and Co|year=1978|isbn=0-7216-4247-0}}
* {{cite book|title=Principles of Physics|author=J.B. Marion, W.F. Hornyak|publisher=Holt-Saunders International Saunders College|year=1984|isbn=4-8337-0195-2}}
* {{cite book|title=Concepts of Modern Physics|edition=4th|author=A. Beiser|publisher=McGraw-Hill (International)|year=1987|isbn=0-07-100144-1}}
* {{cite book|title=University Physics – With Modern Physics|edition=12th|author=H.D. Young, R.A. Freedman|publisher=Addison-Wesley (Pearson International)|year=2008|isbn=0-321-50130-6}}

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