Lorentz-Lorenz
Encyclopedia
The Lorentz–Lorenz equation, also known as the Clausius–Mossotti relation and Maxwell's
formula, relates the refractive index
of a substance to its polarizability
.
The most general form of the Lorentz–Lorenz equation is
where
is the refractive index
,
is the number of molecules per unit volume, and 
is the mean polarizability
.
This equation is only valid for certain crystal structures.
A more specialized form of the Lorentz–Lorenz equation gives the refractive index
of a dilute gas as
where
is the molar refractivity, 
is the pressure of the gas, 
is the universal gas constant, and 
is the (absolute) temperature.
, who discovered it independently in 1878.
James Clerk Maxwell
James Clerk Maxwell of Glenlair was a Scottish physicist and mathematician. His most prominent achievement was formulating classical electromagnetic theory. This united all previously unrelated observations, experiments and equations of electricity, magnetism and optics into a consistent theory...
formula, relates the refractive index
Refractive index
In optics the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium....
of a substance to its polarizability
Polarizability
Polarizability is the measure of the change in a molecule's electron distribution in response to an applied electric field, which can also be induced by electric interactions with solvents or ionic reagents. It is a property of matter...
.
The most general form of the Lorentz–Lorenz equation is
where
is the refractive indexRefractive index
In optics the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium....
,
is the number of molecules per unit volume, and is the mean polarizabilityPolarizability
Polarizability is the measure of the change in a molecule's electron distribution in response to an applied electric field, which can also be induced by electric interactions with solvents or ionic reagents. It is a property of matter...
.
This equation is only valid for certain crystal structures.
A more specialized form of the Lorentz–Lorenz equation gives the refractive index
Refractive index
In optics the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium....
of a dilute gas aswhere
is the molar refractivity, is the pressure of the gas, is the universal gas constant, and is the (absolute) temperature.History
The Lorentz–Lorenz equation is named after the Danish mathematician and scientist Ludvig Lorenz, who published it in 1869, and the Dutch physicist Hendrik LorentzHendrik Lorentz
Hendrik Antoon Lorentz was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for the discovery and theoretical explanation of the Zeeman effect...
, who discovered it independently in 1878.