The Beer-Lambert law is commonly applied to chemical analysis measurements to determine the concentration of chemical species that absorb light. It is often referred to as Beer's law. In physics, the Bouguer–Lambert law is an empirical law which relates the extinction or attenuation of light to the properties of the material through which the light is travelling. It had its first use in astronomical extinction. The fundamental law of extinction is sometimes called the Beer-Bouguer-Lambert law or the Bouguer-Beer-Lambert law or merely the extinction law. The extinction law is also used in understanding attenuation in physical optics, for photons, neutrons, or rarefied gases. In mathematical physics, this law arises as a solution of the BGK equation.
In physics, optical depth or optical thickness is the natural logarithm of the ratio of incident to transmitted radiant power through a material. Thus, the larger the optical depth, the smaller the amount of transmitted radiant power through the material. Spectral optical depth or spectral optical thickness is the natural logarithm of the ratio of incident to transmitted spectral radiant power through a material. Optical depth is dimensionless, and in particular is not a length, though it is a monotonically increasing function of optical path length, and approaches zero as the path length approaches zero. The use of the term "optical density" for optical depth is discouraged.
In physics, attenuation is the gradual loss of flux intensity through a medium. For instance, dark glasses attenuate sunlight, lead attenuates X-rays, and water and air attenuate both light and sound at variable attenuation rates.
UV spectroscopy or UV–visible spectrophotometry refers to absorption spectroscopy or reflectance spectroscopy in part of the ultraviolet and the full, adjacent visible regions of the electromagnetic spectrum. Being relatively inexpensive and easily implemented, this methodology is widely used in diverse applied and fundamental applications. The only requirement is that the sample absorb in the UV-Vis region, i.e. be a chromophore. Absorption spectroscopy is complementary to fluorescence spectroscopy. Parameters of interest, besides the wavelength of measurement, are absorbance (A) or transmittance (%T) or reflectance (%R), and its change with time.
Spectrophotometry is a branch of electromagnetic spectroscopy concerned with the quantitative measurement of the reflection or transmission properties of a material as a function of wavelength. Spectrophotometry uses photometers, known as spectrophotometers, that can measure the intensity of a light beam at different wavelengths. Although spectrophotometry is most commonly applied to ultraviolet, visible, and infrared radiation, modern spectrophotometers can interrogate wide swaths of the electromagnetic spectrum, including x-ray, ultraviolet, visible, infrared, and/or microwave wavelengths.
Absorbance is defined as "the logarithm of the ratio of incident to transmitted radiant power through a sample ". Alternatively, for samples which scatter light, absorbance may be defined as "the negative logarithm of one minus absorptance, as measured on a uniform sample". The term is used in many technical areas to quantify the results of an experimental measurement. While the term has its origin in quantifying the absorption of light, it is often entangled with quantification of light which is “lost” to a detector system through other mechanisms. What these uses of the term tend to have in common is that they refer to a logarithm of the ratio of a quantity of light incident on a sample or material to that which is detected after the light has interacted with the sample.
Transmittance of the surface of a material is its effectiveness in transmitting radiant energy. It is the fraction of incident electromagnetic power that is transmitted through a sample, in contrast to the transmission coefficient, which is the ratio of the transmitted to incident electric field.
In the physical sciences, a partition coefficient (P) or distribution coefficient (D) is the ratio of concentrations of a compound in a mixture of two immiscible solvents at equilibrium. This ratio is therefore a comparison of the solubilities of the solute in these two liquids. The partition coefficient generally refers to the concentration ratio of un-ionized species of compound, whereas the distribution coefficient refers to the concentration ratio of all species of the compound.
In probability theory and statistics, the coefficient of variation (COV), also known as Normalized Root-Mean-Square Deviation (NRMSD), Percent RMS, and relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution. It is defined as the ratio of the standard deviation to the mean , and often expressed as a percentage ("%RSD"). The CV or RSD is widely used in analytical chemistry to express the precision and repeatability of an assay. It is also commonly used in fields such as engineering or physics when doing quality assurance studies and ANOVA gauge R&R, by economists and investors in economic models, and in neuroscience.
In physics, absorption of electromagnetic radiation is how matter takes up a photon's energy — and so transforms electromagnetic energy into internal energy of the absorber. A notable effect is attenuation, or the gradual reduction of the intensity of light waves as they propagate through a medium. Although the absorption of waves does not usually depend on their intensity, in certain conditions (optics) the medium's transparency changes by a factor that varies as a function of wave intensity, and saturable absorption occurs.
In thermodynamics, an activity coefficient is a factor used to account for deviation of a mixture of chemical substances from ideal behaviour. In an ideal mixture, the microscopic interactions between each pair of chemical species are the same and, as a result, properties of the mixtures can be expressed directly in terms of simple concentrations or partial pressures of the substances present e.g. Raoult's law. Deviations from ideality are accommodated by modifying the concentration by an activity coefficient. Analogously, expressions involving gases can be adjusted for non-ideality by scaling partial pressures by a fugacity coefficient.
The visibility is the measure of the distance at which an object or light can be clearly discerned. In meteorology it depends on the transparency of the surrounding air and as such, it is unchanging no matter the ambient light level or time of day. It is reported within surface weather observations and METAR code either in meters or statute miles, depending upon the country. Visibility affects all forms of traffic: roads, railways, sailing and aviation.
In physical organic chemistry, a free-energy relationship or Gibbs energy relation relates the logarithm of a reaction rate constant or equilibrium constant for one series of chemical reactions with the logarithm of the rate or equilibrium constant for a related series of reactions. Free energy relationships establish the extent at which bond formation and breakage happen in the transition state of a reaction, and in combination with kinetic isotope experiments a reaction mechanism can be determined. Free energy relationships are often used to calculate equilibrium constants since they are experimentally difficult to determine.
Opacity is the measure of impenetrability to electromagnetic or other kinds of radiation, especially visible light. In radiative transfer, it describes the absorption and scattering of radiation in a medium, such as a plasma, dielectric, shielding material, glass, etc. An opaque object is neither transparent nor translucent. When light strikes an interface between two substances, in general some may be reflected, some absorbed, some scattered, and the rest transmitted. Reflection can be diffuse, for example light reflecting off a white wall, or specular, for example light reflecting off a mirror. An opaque substance transmits no light, and therefore reflects, scatters, or absorbs all of it. Other categories of visual appearance, related to the perception of regular or diffuse reflection and transmission of light, have been organized under the concept of cesia in an order system with three variables, including opacity, transparency and translucency among the involved aspects. Both mirrors and carbon black are opaque. Opacity depends on the frequency of the light being considered. For instance, some kinds of glass, while transparent in the visual range, are largely opaque to ultraviolet light. More extreme frequency-dependence is visible in the absorption lines of cold gases. Opacity can be quantified in many ways; for example, see the article mathematical descriptions of opacity.
The transmission coefficient is used in physics and electrical engineering when wave propagation in a medium containing discontinuities is considered. A transmission coefficient describes the amplitude, intensity, or total power of a transmitted wave relative to an incident wave.
Diffuse reflectance spectroscopy, or diffuse reflection spectroscopy, is a subset of absorption spectroscopy. It is sometimes called remission spectroscopy. Remission is the reflection or back-scattering of light by a material, while transmission is the passage of light through a material. The word remission implies a direction of scatter, independent of the scattering process. Remission includes both specular and diffusely back-scattered light. The word reflection often implies a particular physical process, such as specular reflection.
The linear attenuation coefficient, attenuation coefficient, or narrow-beam attenuation coefficient characterizes how easily a volume of material can be penetrated by a beam of light, sound, particles, or other energy or matter. A coefficient value that is large represents a beam becoming 'attenuated' as it passes through a given medium, while a small value represents that the medium had little effect on loss. The SI unit of attenuation coefficient is the reciprocal metre (m−1). Extinction coefficient is another term for this quantity, often used in meteorology and climatology. Most commonly, the quantity measures the exponential decay of intensity, that is, the value of downward e-folding distance of the original intensity as the energy of the intensity passes through a unit thickness of material, so that an attenuation coefficient of 1 m−1 means that after passing through 1 metre, the radiation will be reduced by a factor of e, and for material with a coefficient of 2 m−1, it will be reduced twice by e, or e2. Other measures may use a different factor than e, such as the decadic attenuation coefficient below. The broad-beam attenuation coefficient counts forward-scattered radiation as transmitted rather than attenuated, and is more applicable to radiation shielding.
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 M−1⋅cm−1 or L⋅mol−1⋅cm−1. 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.
The Kubelka-Munk theory, devised by Paul Kubelka and Franz Munk, is a fundamental approach to modelling the appearance of paint films. As published in 1931, the theory addresses "the question of how the color of a substrate is changed by the application of a coat of paint of specified composition and thickness, and especially the thickness of paint needed to obscure the substrate". The mathematical relationship involves just two paint-dependent constants.
The concept of the representative layer came about though the work of Donald Dahm, with the assistance of Kevin Dahm and Karl Norris, to describe spectroscopic properties of particulate samples, especially as applied to near-infrared spectroscopy. A representative layer has the same void fraction as the sample it represents and each particle type in the sample has the same volume fraction and surface area fraction as does the sample as a whole. The spectroscopic properties of a representative layer can be derived from the spectroscopic properties of particles, which may be determined by a wide variety of ways. While a representative layer could be used in any theory that relies on the mathematics of plane parallel layers, there is a set of definitions and mathematics, some old and some new, which have become part of representative layer theory.
