# Why is absorbance calculated as $\log_{10}(1/R)$ and not $1-R$?

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”.

• 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.