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In the calculation a, dz and z must be in the same units, say, feet, inches, cm or meters. Note: some authors have added another approximation to this formula, considering dz neglectable compared with z, i.e. dividing by instead of by (z-dz). This induces apreciable errors when calculating coarse stereoacuity at far distance.
where n is the local refractive index as a function of distance along the path C. An electromagnetic wave propagating along a path C has the phase shift over C as if it was propagating a path in a vacuum , length of which, is equal to the optical path length of C .
Optical depth and actual depth, and respectively, can vary widely depending on the absorptivity of the astrophysical environment. Indeed, τ {\displaystyle \tau } is able to show the relationship between these two quantities and can lead to a greater understanding of the structure inside a star .
The use of the term "optical density" for optical depth is discouraged. [1] In chemistry, a closely related quantity called "absorbance" or "decadic absorbance" is used instead of optical depth: the common logarithm of the ratio of incident to transmitted radiant power through a
The skin depth is the distance which the wave can travel before its amplitude reduces by that same factor. The absorption coefficient is related to the penetration depth and skin depth by α = 1 / δ p e n = 2 / δ s k i n . {\displaystyle \alpha =1/\delta _{\mathrm {pen} }=2/\delta _{\mathrm {skin} }.}
In general, solving this integral is quite challenging and only applies for energies above 100 eV. Thus, (semi)empirical formulas were introduced to determine the IMFP. A first approach is to calculate the IMFP by an approximate form of the relativistic Bethe equation for inelastic scattering of electrons in matter.
The most general form of Cauchy's equation is = + + +,where n is the refractive index, λ is the wavelength, A, B, C, etc., are coefficients that can be determined for a material by fitting the equation to measured refractive indices at known wavelengths.
Penetration depth is a measure of how deep light or any electromagnetic radiation can penetrate into a material. It is defined as the depth at which the intensity of the radiation inside the material falls to 1/ e (about 37%) of its original value at (or more properly, just beneath) the surface.