The velocity of propagation of a electromagnetic wave through a solid is given by the frequency-dependent complex refractive index N = n - ik where the real part, n is related to the velocity, and k, the extinction coefficient is related to the decay, or damping of the oscillation amplitude of the incident electric field. By substituting values for ε0 (8.854x10-12 Fm-1) and µ0 (1.257x10-6 Hm-1), the impedance of free space Z0 = (µ0/ε0)½ = 377Ω. The effects of [D.sub.t] and [D.sub.f] on the sound absorption coefficient [alpha] are plotted in Figure 19. If a plane wave of frequency (f) propagates through a solid with velocity (v) in a direction defined by (x), the electric field (E) is described by the following progressive wave equation: Where, (E0)is the incident electric field vector and. (kv), the inverse of the distance at which a monochromatic radiation flux that has frequency ν and forms a parallel beam is attenuated—owing to absorption in a substance—to 1/e (natural absorption coefficient) or 1/10 (decimal absorption coefficient) of its incident intensity. At normal incidence, η = y = Y N, while at oblique incidence where the incident wave becomes polarised. The optical impedance of a material is another useful parameter in considering reflection and transmission of electromagnetic waves across an interface, Z=Ex/Hy=Ey/Hx=(µ0µr/ε0εr)½. The absorption coefficient is measured in cm-1 or m-1, and it is traditionally called the absorption factor in spectrography and some other branches of applied optics. is the displacement at time t after a disturbance, created by the electric field at a point situated at x along the line of propagation. The sound power absorption coeﬃcient α for the test sample at a given frequency is given by α = 1 −R2 Π = 1 − (SWR −1)2 (SWR +1)2 = 4 SWR+ 1 SWR +2. a The fraction of the sound energy (incident at random angles on a surface) which is absorbed or otherwise not reflected by the surface. by the equation c=1/(µ0ε0)½. Hence, ε0ε1E1 = ε0ε2E2 and µ0µ1H1 = µ0µ2H2. The absorption coefficient is therefore described as the reciprocal of the depth of penetration of radiation into a bulk solid, i.e., it is equal to the depth at which the energy of the radiation has decreased by the factor of e-αx, or alternatively, the intensity of the incident radiation is attenuated by the solid to 1/e of its initial value at a distance from the surface boundary defined by λ/4πk. In the case of an absorbing material, the behaviour of a beam of radiation incident in a medium of refractive index n1 on an absorbing medium of complex refractive index n2 = n2-ik2, with an angle of incidence θ1, using Snell's law in complex form is then defined by: Coherence of multiple internal reflections, Find out more about our products and services, Find out more about our research interests, Spectral Characterisation of Infrared Optical Materials and Filters, Absorption and extinction coefficient theory. where . When electromagnetic radiation passes from one medium into another the values of the relative permittivity εr and relative permeability µr must alter according to the characteristics of the materials. The absorption coefficient describes how much light of a given color is absorbed by a material of a given thickness. I i = incident sound intensity (W/m 2). For a short propagation length z , where the overall absorption is small, the absorbed power for an incident power P in is approximately α z P in , and the total transmittance is approximately 1 − α z . ηp = y/cosθ = YN/cosθ and ηs = ycosθ = NY cosθ. Additional optical properties of silicon are given in the page Optical Properties of Silicon. The ratio of the sound energy absorbed by a surface of a medium or material to the sound energy incident on the surface. The optical admittance of free space, Y, is given by Y = 1/Z0 = (ε0/µ0)½ = 2.654x10-3Ω-1. All content on this website, including dictionary, thesaurus, literature, geography, and other reference data is for informational purposes only. https://encyclopedia2.thefreedictionary.com/Absorption+Coefficient. α = I a / I i (1). The sound absorption coefficient is the ratio of absorbed sound intensity in an actual material to the incident sound intensity and can be expressed as. This requires the tangential components of E (electric field vector) and H (magnetic field vector) to be continuous across the boundary, and the normal components of D (electric displacement vector) and B (magnetic flux density vector) to also be continuous across the boundary. If λ is in nm, multiply by 10 7 to get the absorption coefficient in the units of cm-1. In a dielectric with a relative permittivity given by εr and a relative permeability given by µr which is at unity, the admittance is given by y = (ε0εr/µ0)½ = Y εr½ = Y N = Y (n-ik). The velocity of propagation of a electromagnetic wave through a solid is given by the frequency-dependent complex refractive index N = n - ik where the real part, n is related to the velocity, and k, the extinction coefficient is related to the decay, or damping of the oscillation amplitude of the incident electric field. The optical properties of the solid are therefore governed by the interaction between the solid and the electric field of the electromagnetic wave. The velocity of propagation through the solid of complex refractive index N = n - ik is related to the speed of light in a vacuum, c, by V = C / N, then: Therefore, substituting 1/V into equation above produces: is a measure of the damping factor, or extinction coefficient (k).
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