When a beam of light encounters a material, such as a colored liquid or glass, its energy is affected in several ways. Some light bounces off the surface, some is scattered by particles, and the rest either passes straight through or is absorbed by the molecules. Scientists quantify these changes in light intensity using two primary, interrelated terms: transmittance and absorbance. These concepts measure how much light successfully passes through a sample compared to how much light is captured by it.
Understanding Transmittance and Absorbance
Transmittance (T) is a direct measure of the fraction of incident light that successfully travels through a sample and emerges on the other side. It is formally defined as the ratio of the light intensity exiting the sample ($P$) to the intensity of the light entering the sample ($P_0$). This value is commonly expressed as a percentage (%T), ranging from 100% for a perfectly clear medium down to 0% for an opaque substance.
Absorbance (A) is the complementary concept, quantifying the amount of light that the sample retains or stops. These two terms describe the same physical event—the attenuation of light—but from opposite perspectives.
An increase in a sample’s ability to stop light causes a decrease in the amount of light that passes through. Therefore, as transmittance decreases, absorbance increases. However, the relationship is not a simple linear inverse; a sample with 50% transmittance does not have an absorbance of 0.5. The relationship is mathematically complex.
The Mathematical Link: Why the Logarithm Matters
The precise relationship between absorbance and transmittance is defined by a negative logarithmic function: $A = -\log_{10}(T)$. If a sample transmits 10% of the light (T=0.1), its absorbance is 1.0; if it transmits only 1% of the light (T=0.01), its absorbance is 2.0.
The use of a logarithmic scale is a deliberate choice because light attenuation is a non-linear process that occurs exponentially. A linear increase in concentration causes the light intensity to drop by a multiplicative factor, not an additive one. The logarithmic conversion transforms this exponential decay into a linear scale.
This conversion is practical because it expands the scale for samples that absorb a lot of light, allowing for more accurate measurements of small concentration changes in dark solutions. On the absorbance scale, a change from 1.0 to 2.0 represents a tenfold decrease in transmitted light, similar to how a single step on the Richter scale represents a tenfold increase in magnitude. This mathematical structure provides a more workable range for laboratory measurements than the raw transmittance percentage.
The Beer-Lambert Law: The Importance of Absorbance
Scientists prefer to use absorbance (A) over transmittance (T) in quantitative measurements because of its linear link to a sample’s concentration, as established by the Beer-Lambert Law. This law states that the absorbance of a solution is directly proportional to two factors: the concentration ($c$) of the light-absorbing substance and the path length ($l$). The formal expression is $A = \epsilon cl$, where $\epsilon$ is a constant unique to the substance at a specific wavelength.
Because absorbance is directly proportional to concentration, doubling the amount of substance in a solution will predictably double the measured absorbance. This linear relationship makes absorbance useful for determining the concentration of an unknown sample. Scientists can measure the absorbance of solutions with known concentrations, plot the results, and create a straight line.
The absorbance measurement of an unknown sample can then be placed on this line to calculate its concentration. Transmittance lacks this linear relationship with concentration, making it cumbersome for quantitative analysis.
Measuring Light Interaction
The instrument used to measure both transmittance and absorbance is the spectrophotometer. This device works by shining a beam of light of a specific wavelength through a sample contained in a specialized holder called a cuvette. The cuvette typically has a fixed path length of one centimeter, which keeps the path length variable in the Beer-Lambert Law constant.
The spectrophotometer measures the intensity of the light before it enters the sample ($P_0$) and the intensity detected after passing through the sample ($P$). By calculating the ratio of these two intensities ($P/P_0$), the instrument determines the transmittance. Modern spectrophotometers then automatically apply the logarithmic conversion to display the resulting absorbance value.