Question

How are percent transmittance and absorbance related algebraically?

Answer 1

Answer:

So, if all the light passes through a solution without any absorption, then absorbance is zero, and percent transmittance is 100%. If all the light is absorbed, then percent transmittance is zero, and absorption is infinite.

Absorbance is the inverse of transmittance so,

A = 1/T

Beer's law (sometimes called the Beer-Lambert law) states that the absorbance is proportional to the path length, b, through the sample and the concentration of the absorbing species, c:  

A ∝ b · c

As Transmittance, $T =\dfrac{P}{P_0}$

% Transmittance, $\%T=100\times T$

Absorbance,

$A=\log_{10} \dfrac{P_0}{P}\\\\A =\log_{10}\times \dfrac{1}{T}\\\\A=\dfrac{\log_{10} 100}{\%T}\\\\A=(2 - log_{10})\times \%T$

Hence, $A=\log_{10}\times \dfrac{1}{T}$ is the algebraic relation between absorbance and transmittance.