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| | The '''Lorentz–Lorenz equation''', also known as the '''[[Clausius–Mossotti relation]]''' and [[James Clerk Maxwell|Maxwell's]] formula, relates the [[refractive index]] of a substance to its [[polarizability]]. |
| | |
| | The most general form of the Lorentz–Lorenz equation is |
| | :<math> \frac{n^2 - 1}{n^2 + 2} = \frac{4 \pi}{3} N \alpha, </math> |
| | where <math>n</math> is the [[refractive index]], <math>N</math> is the number of molecules per unit volume, and <math>\alpha</math> is the mean [[polarizability]]. |
| | This equation is only valid for certain crystal structures.<ref>Introduction to Solid State Physics/Charles Kittel. - 7th ed. (ISBN 0-471-11181-3) Chapter 13, or 8th ed. (ISBN 0-471-41526-X) p. 464</ref><ref>D. E. Aspnes, Am. J. Phys. 50, 704 (1982)</ref> |
| | |
| | A more specialized form of the Lorentz–Lorenz equation gives the [[refractive index]] <math>n</math> of a dilute gas as |
| | :<math> n \approx \sqrt{1 + \frac{3 A p}{R T}}</math> |
| | where <math>A</math> is the [[molar refractivity]], <math>p</math> is the pressure of the gas, <math>R</math> is the [[universal gas constant]], and <math>T</math> 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 Lorentz]], who discovered it independently in 1878. |
| | |
| | ==See also== |
| | |
| | {{Empty section|date=March 2013}} |
| | |
| | ==References== |
| | |
| | {{reflist}} |
| | |
| | * [[Max Born|Born, Max]], and Wolf, Emil, ''Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light'' (7th ed.), section 2.3.3, Cambridge University Press (1999) ISBN 0-521-64222-1 |
| | |
| | {{DEFAULTSORT:Lorentz-Lorenz Equation}} |
| | [[Category:Optics]] |
Revision as of 02:47, 9 January 2014
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.[1][2]
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.
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 Lorentz, who discovered it independently in 1878.
See also
Template:Empty section
References
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- Born, Max, and Wolf, Emil, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (7th ed.), section 2.3.3, Cambridge University Press (1999) ISBN 0-521-64222-1
- ↑ Introduction to Solid State Physics/Charles Kittel. - 7th ed. (ISBN 0-471-11181-3) Chapter 13, or 8th ed. (ISBN 0-471-41526-X) p. 464
- ↑ D. E. Aspnes, Am. J. Phys. 50, 704 (1982)