Why in the Beer Lambert Law the light intensity attenuation is base 10:
I=I010^(-ecd);
In my memory, the light attenuation should be base e like this
I=I0e^(-ad);
Hi,
https://en.wikipedia.org/wiki/Beer%E2%80%93Lambert_law
' By definition, the transmittance of material sample is related to its optical depth (e) or to its absorbance (10) '
Base "e" would be natural in this case (no pun intended), but no matter what kind of logarithm (i.e. what kind of base you use) it is any way only the constant ascent that is different. The base 10 comes into play, because transmittance absorbance is defined by -log10T where T is the transmittance, which is only under certain circumstances and rarely the same as the absorbance in Beer's law. See e.g. Article Employing Theories Far beyond Their Limits-The Case of the (...
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The mathematical relationships are shown in the following (note that the common (Briggs) logarithm is denoted lg = log10 and the natural logarithm is denoted ln = loge, the latter one not directly used below):
The optical density OD is defined as the absorbance A' written on a logarithmic form by
OD = A’ = log10(1/T) = alog10(e)x = a’x
which is deduced from the Beer-Lambert law given by
I = I0e-ax
where the transmittance T is given by
T = I/I0
where the transmitted radiation intensity I decreases exponentially with the penetration length or depth x, I0 is the incident radiation intensity, and a and a' denote absorption coefficients depending what form is used.
See e.g. chapter 7.6.3 in the following article (may be requested through ResearchGate): B. P. Jelle, ”Solar Radiation Glazing Factors for Window Panes, Glass Structures and Electrochromic Windows in Buildings - Measurement and Calculation”, Solar Energy Materials and Solar Cells, 116, 291-323, 2013.
Related to my above answer, note that in general T + A + R = 1 (100 %) where T = transmittance, A = absorbance and R = reflectance between 0 to 1 (or between 0 to 100 %). That is, the absorbance A is different from the absorbance A’ on the logarithmic form (optical density OD = A’ which is a common output from many spectrophotometers).
Dear Dr. Bjørn Petter Jelle
Thanks for your answer. Your answer is quite clear and informative to me.
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