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While Cauchy's equation (blue line) deviates significantly from the measured refractive indices outside of the visible region (which is shaded red), the Sellmeier equation (green dashed line) does not. The Sellmeier equation is an empirical relationship between refractive index and wavelength for a particular transparent medium.
Wolfgang Sellmeier was a German theoretical physicist who made major contributions to the understanding of the interactions between light and matter. [1] In 1872 he published his seminal work Ueber die durch die Aetherschwingungen erregten Mitschwingungen der Körpertheilchen und deren Rückwirkung auf die ersteren, besonders zur Erklärung der Dispersion und ihrer Anomalien. [2]
The primary difference between a computer algebra system and a traditional calculator is the ability to deal with equations symbolically rather than numerically. The precise uses and capabilities of these systems differ greatly from one system to another, yet their purpose remains the same: manipulation of symbolic equations.
A. R. Forouhi and I. Bloomer deduced dispersion equations for the refractive index, n, and extinction coefficient, k, which were published in 1986 [1] and 1988. [2] The 1986 publication relates to amorphous materials, while the 1988 publication relates to crystalline.
In optics, Cauchy's transmission equation is an empirical relationship between the refractive index and wavelength of light for a particular transparent material. It is named for the mathematician Augustin-Louis Cauchy , who originally defined it in 1830 in his article "The refraction and reflection of light".
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The general formula is (Si x O 3x) 2x−, where one or more silicon atoms can be replaced by other 4-coordinated atom(s). The silicon:oxygen ratio is 1:3. The silicon:oxygen ratio is 1:3. Double rings have the formula (Si 2 x O 5 x ) 2 x − or a 2:5 ratio.
The idealized equation involving a trisilicate and sulfuric acid is: Na 2 Si 3 O 7 + H 2 SO 4 3 SiO 2 + Na 2 SO 4 + H 2 O {\displaystyle {\ce {Na2Si3O7 + H2SO4 -> 3 SiO2 + Na2SO4 + H2O}}} Approximately one billion kilograms/year (1999) of silica were produced in this manner, mainly for use for polymer composites – tires and shoe soles.