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Absorption coefficient | Table of contents |
▶ Absorption coefficient, ambiguity
▶ Absorption coefficient, and absorbance
▶ Absorption coefficient, and refractive index
▶ Absorption coefficient, chlorophyll-specific
▶ Absorption coefficient, concentration-specific
▶ Absorption coefficient, decadic
▶ Absorption coefficient, definition
▶ Absorption coefficient, dispersions
▶ Absorption coefficient, mass-specific
▶ Absorption coefficient, mass-specific, aquatic sciences
▶ Absorption coefficient, molar
▶ Absorption coefficient, natural
▶ Absorption coefficient, particle mass-specific
▶ Absorption coefficient, particulate media
Absorption coefficient, ambiguity
Absorption coefficient, and absorbance
See also Braslavsky SE 2007
Absorption coefficient, and refractive index
For a homogeneous material, the absorption coefficient is related to the imaginary part of the complex refractive refractive index, m", of the material as follows:
a(λ) = 4π m"(λ) / λ | (1) |
where λ is the wavelength of light in vacuum.
See also Eq. 2 in Refractive index.
Absorption coefficient, chlorophyll-specific
▶ Absorption coefficient, mass-specific, aquatic sciences
■ Absorption coefficient, mass-specific
■ Absorption coefficient, concentration-specific
Absorption coefficient, concentration-specific
Absorption coefficient, a, of light in a medium is related to the concentration in that medium of the light-absorption agent, as well as to optical properties of the agent. Hence, by normalizing a to the concentration of that agent, one should be able to focus on the effect of those properties on light absorption by the medium. This leads to the concept of the concentration-specific absorption coefficient, exemplified by the mass-specific absorption coefficient and the molar absorption coefficient.
■ Absorption coefficient, mass-specific
■ Absorption coefficient, molar
Absorption coefficient, decadic
The absorption coefficient is generally expressed by solving Eq. 3 in Absorption coefficient, definition by using the natural logarithm scale. However, the decimal logarithm scale is sometimes used instead. This latter approach leads to the decadic absorption coefficient, a_{10} (for example, Litjens RAJ et al 1999, Quickenden TI and Irvin 1980). The decadic absorption coefficient, a_{10}, is related to the absorption coefficient, a, as follows:
a_{10} = a / ln10 | (2) |
Thus, it is important to understand which definition of the absorption coefficient is used in a publication, because each leads to a different numerical value although the units (for example, m^{-1}) may be the same.
■ Absorption coefficient, natural
Absorption coefficient, definition
Absorption coefficient of light in a medium is customarily denoted by a [length^{-1}] and defined by the following equation:
a = - (1 / z) ln[Φ(z) / Φ(0)] | (1) |
where Φ [power] is the power of light in a collimated beam, z [length] is the distance. Notation "[power]" means the unit of power, for example, Watt. The above equation is a solution of the following equation (the Lambert law for absorption):
Φ(z) = Φ(0) e^{ -az} | (2) |
which is a solution of a differential equation describing the loss of power of light propagating in a homogenous medium:
dΦ(z) = -aΦ(z) dz | (3) |
The inverse of the absorption coefficient is referred to as the absorption length. It is the average distance a photon can travel in a medium before being absorbed.
Absorption coefficient, dispersions
As noted by Duysens LNM 1956, the absorption coefficient spectrum of a dispersion of pigmented particles may differ from the absorption coefficient spectrum of the pigment solution. This pigment packaging (for example, Finlay JC and Foster 2004 - red blood cells, and Morel A and Bricaud 1981 - phytoplankton) causes a flattening of the absorption spectrum of the dispersion as compared to that of the pigment solution.
Absorption coefficient, mass-specific
The mass-specific absorption coefficient [length^{2} mass^{-1}] is defined as follows:
a_{m} = a / C_{mv} | (1) |
where a is the absorption coefficient, and C_{mv} [mass length^{-3}] is the mass-per-volume concentration of a light absorbing agent. That agent can be dissolved in the medium, and/or dispersed as particles.
▶ Absorption coefficient, mass-specific, aquatic sciences
■ Absorption coefficient, concentration-specific
■ Absorption coefficient, dispersions
Absorption coefficient, mass-specific, aquatic sciences
In aquatic sciences, the mass-specific absorption coefficients include the particle mass-specific absorption coefficient, a_{p}^{*}, (for example, Wozniak SB et al 2010) and the chlorophyll-specific absorption coefficient, a_{chl}^{*}, (for example, Bricaud A et al 1995) and are typically expressed in m^{2} g^{-1} and m^{2} mg^{-1}, respectively.
◀ Absorption coefficient, mass-specific
■ Absorption coefficient, concentration-specific
Absorption coefficient, molar
The molar absorption coefficient, usually expressed in dm^{3} mol^{-1} cm^{-1} in the spectroscopic literature (for example, Braslavsky SE 2007), is defined as follows:
a_{M} = a / C_{M} | (1) |
where a is the absorption coefficient defined by Eq 1 in Absorption coefficient, definition and C_{M} [mol dm^{-3}] is the molar concentration of the light absorbing agent.
The molar absorption coefficient of water, as well as that of other light absorbing media, depends on temperature. This dependence is due to changes in the specific density of the medium with temperature.
Indeed, note that C_{M} can be expressed as follows:
C_{M} = ρ / M | (2) |
where ρ is the specific density [g dm^{-3}] and M is the molar mass [g mol^{-1}]
Although the molar mass of water, M = 18.01528 g / mol, is constant, the specific density of water changes with temperature. For example, at 5 °C, the specific density of water, ρ = 1000 g dm^{-3}, while at 25 °C ρ = 997.1 g dm^{-3}. Hence, at 5 °C the molar concentration of water, C_{M} = (1000 / 18.01528 ) = 55.5084 mol / dm^{-3}, while at 25 °C C_{M} = (997.1 / 18.01528 ) = 55.3475 mol / dm^{-3}.
■ Absorption coefficient, mass-specific
■ Absorption coefficient, concentration-specific
Absorption coefficient, natural
▶ Absorption coefficient, definition
Absorption coefficient, of
water, see Absorption coefficient of water
Absorption coefficient, particle mass-specific
▶ Absorption coefficient, mass-specific, aquatic sciences
■ Absorption coefficient, concentration-specific
Absorption coefficient, particulate media
▶ Absorption coefficient, dispersions
CITATION: Jonasz M. 2006. Absorption coefficient (www.mjcopticaltech.com/Publications/AbsCf.php). |
Published: 13-Jan-2006 |
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