List of optics equations
This article summarizes equations in the theory of photonics, including geometric optics, physical optics, radiometry, diffraction, and interferometry.
Definitions
Geometric optics (luminal rays)
General fundamental quantities
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
Physical optics (EM luminal waves)
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
Radiometry
![](http://upload.wikimedia.org/wikipedia/commons/thumb/0/00/Flux_and_solid_angle.svg/275px-Flux_and_solid_angle.svg.png)
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)
Equations
Luminal electromagnetic waves
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:
Cononical momentum:
Irradiance, light intensity - = time averaged poynting vector
- I = irradiance
- I0 = intensity of source
- P0 = power of point source
- Ω = solid angle
- r = radial position from source
At a spherical surface:
Doppler effect for light (relativistic) Cherenkov radiation, cone angle - n = refractive index
- v = speed of particle
- θ = cone angle
Electric and magnetic amplitudes - E = electric field
- H = magnetic field strength
For a dielectric EM wave components Electric Magnetic
Geometric optics
Physical situation Nomenclature Equations Critical angle (optics) - n1 = refractive index of initial medium
- n2 = refractive index of final medium
- θc = critical angle
Thin lens equation - f = lens focal length
- x1 = object length
- x2 = image length
- r1 = incident curvature radius
- r2 = refracted curvature radius
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:
- ε = permittivity of medium,
- μ = permeability of medium,
- λ = wavelength of light in medium,
- v = speed of light in media.
Polarization
Physical situation Nomenclature Equations Angle of total polarisation - θB = Reflective polarization angle, Brewster's angle
intensity from polarized light, Malus's law - I0 = Initial intensity,
- I = Transmitted intensity,
- θ = Polarization angle between polarizer transmission axes and electric field vector
Diffraction and interference
Property or effect Nomenclature Equation Thin film in air - n1 = refractive index of initial medium (before film interference)
- n2 = refractive index of final medium (after film interference)
- Minima:
- Maxima:
The grating equation - a = width of aperture, slit width
- α = incident angle to the normal of the grating plane
Rayleigh's criterion Bragg's law (solid state diffraction) - d = lattice spacing
- δ = phase difference between two waves
- For constructive interference:
- For destructive interference:
where
Single slit diffraction intensity - I0 = source intensity
- Wave phase through apertures
N-slit diffraction (N ≥ 2) - d = centre-to-centre separation of slits
- N = number of slits
- Phase between N waves emerging from each slit
N-slit diffraction (all N) Circular aperture intensity - a = radius of the circular aperture
- J1 is a Bessel function
Amplitude for a general planar aperture Cartesian and spherical polar coordinates are used, xy plane contains aperture - A, amplitude at position r
- r' = source point in the aperture
- Einc, magnitude of incident electric field at aperture
Near-field (Fresnel) Far-field (Fraunhofer)
Huygen-Fresnel-Kirchhoff principle - r0 = position from source to aperture, incident on it
- r = position from aperture diffracted from it to a point
- α0 = 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
- = unit normal vector to the aperture
Kirchhoff's diffraction formula
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.
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
See also
- Defining equation (physics)
- Defining equation (physical chemistry)
- List of electromagnetism equations
- List of equations in classical mechanics
- List of equations in gravitation
- List of equations in nuclear and particle physics
- List of equations in quantum mechanics
- List of equations in wave theory
- List of relativistic equations
Sources
- P.M. Whelan; M.J. Hodgeson (1978). Essential Principles of Physics (2nd ed.). John Murray. ISBN 0-7195-3382-1.
- G. Woan (2010). The Cambridge Handbook of Physics Formulas. Cambridge University Press. ISBN 978-0-521-57507-2.
- A. Halpern (1988). 3000 Solved Problems in Physics, Schaum Series. Mc Graw Hill. ISBN 978-0-07-025734-4.
- R.G. Lerner; G.L. Trigg (2005). Encyclopaedia of Physics (2nd ed.). VHC Publishers, Hans Warlimont, Springer. pp. 12–13. ISBN 978-0-07-025734-4.
- C.B. Parker (1994). McGraw Hill Encyclopaedia of Physics (2nd ed.). McGraw Hill. ISBN 0-07-051400-3.
- P.A. Tipler; G. Mosca (2008). Physics for Scientists and Engineers: With Modern Physics (6th ed.). W.H. Freeman and Co. ISBN 978-1-4292-0265-7.
- L.N. Hand; J.D. Finch (2008). Analytical Mechanics. Cambridge University Press,. ISBN 978-0-521-57572-0.
{{cite book}}
: CS1 maint: extra punctuation (link) - T.B. Arkill; C.J. Millar (1974). Mechanics, Vibrations and Waves. John Murray,. ISBN 0-7195-2882-8.
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: CS1 maint: extra punctuation (link) - H.J. Pain (1983). The Physics of Vibrations and Waves (3rd ed.). John Wiley & Sons,. ISBN 0-471-90182-2.
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: CS1 maint: extra punctuation (link) - J.R. Forshaw; A.G. Smith (2009). Dynamics and Relativity. Wiley,. ISBN 978-0-470-01460-8.
{{cite book}}
: CS1 maint: extra punctuation (link) - G.A.G. Bennet (1974). Electricity and Modern Physics (2nd ed.). Edward Arnold (UK). ISBN 0-7131-2459-8.
- I.S. Grant; W.R. Phillips; Manchester Physics (2008). Electromagnetism (2nd Edition). John Wiley & Sons. ISBN 978-0-471-92712-9.
- D.J. Griffiths (2007). Introduction to Electrodynamics (3rd ed.). Pearson Education, Dorling Kindersley,. ISBN 81-7758-293-3.
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: CS1 maint: extra punctuation (link)
Further reading
- L.H. Greenberg (1978). Physics with Modern Applications. Holt-Saunders International W.B. Saunders and Co. ISBN 0-7216-4247-0.
- J.B. Marion; W.F. Hornyak (1984). Principles of Physics. Holt-Saunders International Saunders College. ISBN 4-8337-0195-2.
- A. Beiser (1987). Concepts of Modern Physics (4th ed.). McGraw-Hill (International). ISBN 0-07-100144-1.
- H.D. Young; R.A. Freedman (2008). University Physics – With Modern Physics (12th ed.). Addison-Wesley (Pearson International). ISBN 0-321-50130-6.