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Optical cross section of a flat mirror with a given reflectivity at a particular wavelength () can be expressed by the formula = Where is the cross sectional diameter of the beam. Note that the direction of the light has to be perpendicular to the mirror surface for this formula to be valid, else the return from the mirror would no longer go ...
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:
The cross section can then be calculated, using the diffraction coefficients, with the physical theory of diffraction or other high frequency method, combined with physical optics to include the contributions from illuminated smooth surfaces and Fock calculations to calculate creeping waves circling around any smooth shadowed parts.
The optical path difference between the paths taken by two identical waves can then be used to find the phase change. Finally, using the phase change, the interference between the two waves can be calculated. Fermat's principle states that the path light takes between two points is the path that has the minimum optical path length.
Ray tracing of a beam of light passing through a medium with changing refractive index.The ray is advanced by a small amount, and then the direction is re-calculated. Ray tracing works by assuming that the particle or wave can be modeled as a large number of very narrow beams (), and that there exists some distance, possibly very small, over which such a ray is locally straight.
Rayleigh–Gans approximation has been applied on the calculation of the optical cross sections of fractal aggregates. [6] The theory was also applied to anisotropic spheres for nanostructured polycrystalline alumina and turbidity calculations on biological structures such as lipid vesicles [7] and bacteria.
The index ellipsoid is not to be confused with the index surface, whose radius vector (from the origin) in any direction is indeed the refractive index for propagation in that direction; for a birefringent medium, the index surface is the two-sheeted surface whose two radius vectors in any direction have lengths equal to the major and minor semiaxes of the diametral section of the index ...
where Q is the efficiency factor of scattering, which is defined as the ratio of the scattering cross-section and geometrical cross-section πa 2. The term p = 4πa( n − 1)/λ has as its physical meaning the phase delay of the wave passing through the centre of the sphere, where a is the sphere radius, n is the ratio of refractive indices ...