38
K. D. Dahm and D. J. Dahm
3.1 Early Explorations of Absorption, Scattering,
and Extinction
The eighteenth-century contributions of Pierre Bouguer were foundational in developing our current understanding of how light interacts with matter. Bouguer studied
the phenomenon of light becoming dimmer as it passed through the atmosphere.
He discovered a first-order logarithmic relationship between the remaining intensity
of the light and the thickness of atmosphere it had penetrated [1]. Using modern
terminology, one way to express this is:
I
I 0
= exp(− ∈ t)
(3.1)
In which I 0 is the intensity of the light at its source, I is the intensity of light
that reaches the detector, and t is the thickness of atmosphere. The ε in Eq. 3.1 is a
parameter that has different values for different wavelengths, but what specifically
does it measure? Bouguer himself did not necessarily attribute the dimming of the
light to a particular physical phenomenon. We now use the term “extinction” for
the total observed attenuation of a beam, and thus ε quantifies the ability of the
atmosphere to “extinguish” a specific wavelength of light. Indeed, ε has been termed
the “extinction coefficient.” [2]. We now understand that both absorption and scatter
contribute to extinction in an experiment like Bouguer’s. If one is looking at a distant
object (e.g., the sun), any light that was either scattered from its original path or
absorbed by the air molecules does not reach one’s eyes.
Another foundational body of work was that of Beer in the nineteenth century,
which demonstrated that chemical compounds have an ability to absorb light at particular wavelengths, and that the extent of the “absorbance” of the light is proportional
to the concentration of the absorber. Mathematically, one can define absorbance as:
Absorbance = −log 10
I
I 0
(3.2)
I 0 again represents the intensity of incident light, I represents the amount of light
that reached the detector, and consequently, I/I 0 is the fraction of the incident light
that penetrated the sample and was detected. When this fraction is 1, the “absorbance”
is by definition 0. As the fraction of detected light decreases, the “absorbance” as
defined in Eq. 3.2 increases, representing the inference that more light has been
absorbed. Note that the absorbance is not equal to the “fraction of light that was
absorbed”; absorbance can be greater than one and it approaches infinity as I/I 0
approaches zero. The quantity defined in Eq. 3.2 is sometimes called the “decadic
absorbance” to emphasize that base 10 logarithms were used, since it is also possible
to use natural logarithms.
“Beer’s Law” can be expressed as [3]:
K. D. Dahm and D. J. Dahm
3.1 Early Explorations of Absorption, Scattering,
and Extinction
The eighteenth-century contributions of Pierre Bouguer were foundational in developing our current understanding of how light interacts with matter. Bouguer studied
the phenomenon of light becoming dimmer as it passed through the atmosphere.
He discovered a first-order logarithmic relationship between the remaining intensity
of the light and the thickness of atmosphere it had penetrated [1]. Using modern
terminology, one way to express this is:
I
I 0
= exp(− ∈ t)
(3.1)
In which I 0 is the intensity of the light at its source, I is the intensity of light
that reaches the detector, and t is the thickness of atmosphere. The ε in Eq. 3.1 is a
parameter that has different values for different wavelengths, but what specifically
does it measure? Bouguer himself did not necessarily attribute the dimming of the
light to a particular physical phenomenon. We now use the term “extinction” for
the total observed attenuation of a beam, and thus ε quantifies the ability of the
atmosphere to “extinguish” a specific wavelength of light. Indeed, ε has been termed
the “extinction coefficient.” [2]. We now understand that both absorption and scatter
contribute to extinction in an experiment like Bouguer’s. If one is looking at a distant
object (e.g., the sun), any light that was either scattered from its original path or
absorbed by the air molecules does not reach one’s eyes.
Another foundational body of work was that of Beer in the nineteenth century,
which demonstrated that chemical compounds have an ability to absorb light at particular wavelengths, and that the extent of the “absorbance” of the light is proportional
to the concentration of the absorber. Mathematically, one can define absorbance as:
Absorbance = −log 10
I
I 0
(3.2)
I 0 again represents the intensity of incident light, I represents the amount of light
that reached the detector, and consequently, I/I 0 is the fraction of the incident light
that penetrated the sample and was detected. When this fraction is 1, the “absorbance”
is by definition 0. As the fraction of detected light decreases, the “absorbance” as
defined in Eq. 3.2 increases, representing the inference that more light has been
absorbed. Note that the absorbance is not equal to the “fraction of light that was
absorbed”; absorbance can be greater than one and it approaches infinity as I/I 0
approaches zero. The quantity defined in Eq. 3.2 is sometimes called the “decadic
absorbance” to emphasize that base 10 logarithms were used, since it is also possible
to use natural logarithms.
“Beer’s Law” can be expressed as [3]: