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Mathematical Descriptions Of Opacity
When an electromagnetic wave travels through a medium in which it gets attenuated (this is called an " opaque" or " attenuating" medium), it undergoes exponential decay as described by the Beer–Lambert law. However, there are many possible ways to characterize the wave and how quickly it is attenuated. This article describes the mathematical relationships among: * attenuation coefficient; * penetration depth and skin depth; * complex angular wavenumber and propagation constant; * complex refractive index; * complex electric permittivity; * AC conductivity (susceptance). Note that in many of these cases there are multiple, conflicting definitions and conventions in common use. This article is not necessarily comprehensive or universal. Background: unattenuated wave Description An electromagnetic wave propagating in the +''z''-direction is conventionally described by the equation: \mathbf(z, t) = \operatorname \left mathbf_0 e^\right! , where *E0 is a vector in the ''x''- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electromagnetic Wave
In physics, electromagnetic radiation (EMR) is a self-propagating wave of the electromagnetic field that carries momentum and radiant energy through space. It encompasses a broad spectrum, classified by frequency or its inverse, wavelength, ranging from radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. All forms of EMR travel at the speed of light in a vacuum and exhibit wave–particle duality, behaving both as waves and as discrete particles called photons. Electromagnetic radiation is produced by accelerating charged particles such as from the Sun and other celestial bodies or artificially generated for various applications. Its interaction with matter depends on wavelength, influencing its uses in communication, medicine, industry, and scientific research. Radio waves enable broadcasting and wireless communication, infrared is used in thermal imaging, visible light is essential for vision, and higher-energy radiation, such as X ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angular Wavenumber
In the physical sciences, the wavenumber (or wave number), also known as repetency, is the spatial frequency of a wave. Ordinary wavenumber is defined as the number of wave cycles divided by length; it is a physical quantity with dimension of reciprocal length, expressed in SI units of cycles per metre or reciprocal metre (m−1). Angular wavenumber, defined as the wave phase divided by time, is a quantity with dimension of angle per length and SI units of radians per metre. They are analogous to temporal frequency, respectively the '' ordinary frequency'', defined as the number of wave cycles divided by time (in cycles per second or reciprocal seconds), and the ''angular frequency'', defined as the phase angle divided by time (in radians per second). In multidimensional systems, the wavenumber is the magnitude of the ''wave vector''. The space of wave vectors is called ''reciprocal space''. Wave numbers and wave vectors play an essential role in optics and the physics of w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Absorption Cross Section
In physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ..., absorption cross-section is a measure of the probability of an absorption process. More generally, the term cross section (physics), cross-section is used in physics to quantify the probability of a certain particle-particle interaction, e.g., scattering, absorption (electromagnetic radiation), electromagnetic absorption, etc. (Note that light in this context is described as consisting of elementary particle, particles, i.e., photons.) A typical absorption cross-section has units of cm2⋅molecule−1. In honor of the fundamental contribution of Maria Goeppert Mayer to this area, the unit for the two-photon absorption cross section is named the "GM". One GM is 10−50 cm4⋅s⋅photon−1. In the context of ozone ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mass Attenuation Coefficient
The mass attenuation coefficient, or mass narrow beam attenuation coefficient of a material is the attenuation coefficient normalized by the density of the material; that is, the attenuation per unit mass (rather than per unit of distance). Thus, it characterizes how easily a mass of material can be penetrated by a beam of light, sound, particles, or other energy or matter. In addition to visible light, mass attenuation coefficients can be defined for other electromagnetic radiation (such as X-rays), sound, or any other beam that can be attenuated. The SI unit of mass attenuation coefficient is the square metre per kilogram (). Other common units include cm2/g (the most common unit for X-ray mass attenuation coefficients) and L⋅g−1⋅cm−1 (sometimes used in solution chemistry). Mass extinction coefficient is an old term for this quantity. The mass attenuation coefficient can be thought of as a variant of absorption cross section where the effective area is defined per unit m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Molar Absorptivity
In chemistry, the molar absorption coefficient or molar attenuation coefficient () is a measurement of how strongly a chemical species absorbs, and thereby attenuates, light at a given wavelength. It is an intrinsic property of the species. The SI unit of molar absorption coefficient is the square metre per mole (), but in practice, quantities are usually expressed in terms of −1⋅cm−1 or L⋅mol−1⋅cm−1 (the latter two units are both equal to ). In older literature, the cm2/mol is sometimes used; 1 M−1⋅cm−1 equals 1000 cm2/mol. The molar absorption coefficient is also known as the molar extinction coefficient and molar absorptivity, but the use of these alternative terms has been discouraged by the IUPAC. Beer–Lambert law The absorbance of a material that has only one absorbing species also depends on the pathlength and the concentration of the species, according to the Beer–Lambert law :A = \varepsilon c\ell, where * is the ''molar absorption coef ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Conjugate
In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. That is, if a and b are real numbers, then the complex conjugate of a + bi is a - bi. The complex conjugate of z is often denoted as \overline or z^*. In polar form, if r and \varphi are real numbers then the conjugate of r e^ is r e^. This can be shown using Euler's formula. The product of a complex number and its conjugate is a real number: a^2 + b^2 (or r^2 in polar coordinates). If a root of a univariate polynomial with real coefficients is complex, then its complex conjugate is also a root. Notation The complex conjugate of a complex number z is written as \overline z or z^*. The first notation, a vinculum, avoids confusion with the notation for the conjugate transpose of a matrix, which can be thought of as a generalization of the complex conjugate. The second is preferred in physics, where ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electrical Impedance
In electrical engineering, impedance is the opposition to alternating current presented by the combined effect of Electrical_resistance, resistance and Electrical_reactance, reactance in a electrical circuit, circuit. Quantitatively, the impedance of a two-terminal Electrical element, circuit element is the ratio of the phasor, complex representation of the Sine wave, sinusoidal voltage between its terminals, to the complex representation of the current flowing through it. In general, it depends upon the frequency of the sinusoidal voltage. Impedance extends the concept of Electrical resistance, resistance to alternating current (AC) circuits, and possesses both Euclidean vector, magnitude and Phase (waves), phase, unlike resistance, which has only magnitude. Impedance can be represented as a complex number, with the same units as resistance, for which the SI unit is the ohm (). Its symbol is usually , and it may be represented by writing its magnitude and phase in the Polar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intensity (physics)
In physics and many other areas of science and engineering the intensity or flux of radiant energy is the Power (physics), power transferred per unit area, where the area is measured on the plane perpendicular to the direction of propagation of the energy. In the SI system, it has units watts per square metre (W/m2), or kilogram, kg⋅second, s−3 in SI base unit, base units. Intensity is used most frequently with waves such as acoustic waves (sound), matter waves such as electrons in electron microscopes, and electromagnetic waves such as light or radio waves, in which case the time averaging, ''average'' power transfer over one Period (physics), period of the wave is used. ''Intensity'' can be applied to other circumstances where energy is transferred. For example, one could calculate the intensity of the kinetic energy carried by drops of water from a garden sprinkler. The word "intensity" as used here is not synonymous with "wikt:strength, strength", "wikt:amplitude, amplitude ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Refractive Index
In optics, the refractive index (or refraction index) of an optical medium is the ratio of the apparent speed of light in the air or vacuum to the speed in the medium. The refractive index determines how much the path of light is bent, or refraction, refracted, when entering a material. This is described by Snell's law of refraction, , where and are the angle of incidence (optics), angle of incidence and angle of refraction, respectively, of a ray crossing the interface between two media with refractive indices and . The refractive indices also determine the amount of light that is reflectivity, reflected when reaching the interface, as well as the critical angle for total internal reflection, their intensity (Fresnel equations) and Brewster's angle. The refractive index, n, can be seen as the factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values: the speed of light in a medium is , and similarly the wavelength in that me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Speed Of Light
The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time interval of second. The speed of light is invariant (physics), the same for all observers, no matter their relative velocity. It is the upper limit for the speed at which Information#Physics_and_determinacy, information, matter, or energy can travel through Space#Relativity, space. All forms of electromagnetic radiation, including visible light, travel at the speed of light. For many practical purposes, light and other electromagnetic waves will appear to propagate instantaneously, but for long distances and sensitive measurements, their finite speed has noticeable effects. Much starlight viewed on Earth is from the distant past, allowing humans to study the history of the universe by viewing distant objects. When Data communication, comm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
