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### Quantitative Photometric Analysis Using Absorbance Ratios: Optimizing Peak Transmittances

*Volume 26, Number 3 (June 1972) Page 405-406*

McDowell, Robin S.

The relation between given relative errors in transmittance (*T = I/I*_{o}) and absorbance (*A* = -log *T*) in photometric analysis is

*A*/

*A*= - (log

*e*)Δ

*T*(10

^{A}/

*A*). (1)If Beer's law holds, the concentration of a substance is given by

*c*=

*A*/

*ab*,where

*a*is its absorptivity at the wave length used and

*b*is the path length; the relative error in the concentration, Δ

*c/c*, is then just Δ

*A/A*. If it is further assumed that the error in measuring the transmittance is independent of

*T*(i.e., that Δ

*T*is constant), then differentiation of Eq. (1) shows that Δ

*c/c*is minimized for

*A*= log

*e*= 0.43, or

*T*=

*e*

^{−1}= 0.37, at which point | Δ

*c/c*| =

*e*Δ

*T*= 2.72Δ

*T*. The minimum is a rather flat one, and the useful analytical range is generally quoted as about 20 to 60 %

*T*.