According to Lambert Beers law, the absorbance ($A$) of a sample at a given wavelength can be described in terms of its transmittance ($T$) according to:

$A = \log_{10}(1/T)$

In near-infrared spectroscopy, when measuring how light is reflected off of opaque samples, absorbance is commonly calculated using the same equation, but by simply substituting the transmittance for reflectance:

$A = \log_{10}(1/R)$

Supposedly, this only works if the sample being measured is thick enough for the transmittance to be zero. The only motivation I have been able to find in literature for changing $T$ to $R$ is: “reflectance is analogous to transmittance in NIR spectroscopy”.

What I struggle to understand about this is:

  • Why would it be valid to simply change the transmittance into reflectance when this is not mentioned in Lambert Beers law?
  • Since light hitting a sample can either

    a) transmit through it;

    b) absorb into it;

    c) reflect off of it.

    Why is the absorbance simply not calculated as $A = 1 – R$ when the transmittance is assumed to be $0$? (Since $T + A + R$ has to equal $1$).


These are two different kinds of looking at absorption. I have a remote sensing background, and we usually look at it from a conservation of energy point of view, stating that the radiation that hits a surface is partly reflected, partly transmitted, and partly absorbed, and that $R+T+A=1$. These are unitless fractions.

If you are interested in absorption in Lambert-Beer's Law, you can transform $A=\log_{10}(1/R)$ for opaque bodies. You can write Lambert-Beer's Law as $I=I_0 e^{k\cdot c\cdot d}$ where
$I$ is radiation intensity after passing through the turbid medium,
$I_0$ is radiation intensity before,
$k$ is the specific absorption coefficient of a pure solvent,
$c$ is its concentration, and
$d$ is the distance traveled through the medium.

Now we can call $k\cdot c$ the absorption coefficient and see that it must have a unit, e.g. $\mathrm{cm^{-1}}$. It can also have much higher values than $1$.

I can't answer why $R$ and $T$ are sometimes simply interchanged. In soil spectroscopy, the $A = \lg(1/R)$ is quite common, and soil is opaque.


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