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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 the superscript k+1 denotes the next iteration, which is to be calculated and k is the last calculated result. This is in essence a Matrix splitting method, similar to the Jacobi method , applied to the large, sparse system arising when solving for all pixels simultaneously [ citation needed ] .
From equations and , if ϵ is fixed instead of μ, then Y becomes inversely proportional to n, with the result that the subscripts 1 and 2 in equations to are interchanged (due to the additional step of multiplying the numerator and denominator by n 1 n 2).
The subscripts i and s denote the incident and scattered waves. The first equation is the result of the application of the conservation of energy to the system of the incident photon, the scattered photon, and the interacting phonon. Applying conservation of energy also sheds light upon the frequency regime in which Brillouin scattering occurs.
In this equation, α (Greek letter "alpha") is the measured rotation in degrees, l is the path length in decimeters, and ρ (Greek letter "rho") is the density of the liquid in g/mL, for a sample at a temperature T (given in degrees Celsius) and wavelength λ (in nanometers).
The optic equation, permitting but not requiring integer solutions, appears in several contexts in geometry. In a bicentric quadrilateral , the inradius r , the circumradius R , and the distance x between the incenter and the circumcenter are related by Fuss' theorem according to
The term Mie solution is also used for solutions of Maxwell's equations for scattering by stratified spheres or by infinite cylinders, or other geometries where one can write separate equations for the radial and angular dependence of solutions.
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".