Spectrophotometry is a fundamental laboratory technique used across chemistry and biology to quantify how a substance interacts with light. This analytical method measures the intensity of light before it enters a sample and compares it to the intensity after it has passed through the sample. Scientists primarily use two related metrics to describe this interaction: transmittance and absorbance.
Understanding Transmittance and Absorbance
Transmittance (T) is defined as the fraction of the original light that successfully passes through a substance. If a light beam starts with intensity I_0 and the transmitted light has intensity I, transmittance is the ratio T = I / I_0. This value is often expressed as percent transmittance (%T), ranging from 0% (no light passes through) to 100% (all light passes through).
Absorbance (A), sometimes called optical density, measures the amount of light retained or blocked by the sample. It is the inverse relationship to transmittance, quantifying how much light the substance has taken in. A substance with high absorbance is highly opaque to the measured light wavelength. Spectrophotometers initially measure transmitted light, but this value is converted to the absorbance reading, which is the preferred metric for scientific analysis.
The Mathematical Conversion Formula
To convert the measured transmittance value into absorbance, a logarithmic relationship is used. Absorbance is mathematically defined as the negative logarithm (base 10) of the transmittance (T) expressed as a decimal fraction. The fundamental relationship is A = -log(T), or equivalently, A = log(1/T).
If the instrument output is given as percent transmittance (%T), the formula must be adjusted for the percentage scale. Since T = %T / 100, the expression simplifies to A = log(100 / %T), which is equivalent to A = 2 – log(%T). For instance, if a sample transmits 25% of the incident light, the absorbance is calculated as 2 – log(25), yielding an absorbance of 0.60.
The reason for this logarithmic conversion lies in the physical nature of light attenuation. When light passes through a uniform material, its intensity decreases exponentially with the distance traveled and the concentration of the absorbing substance. The logarithm serves to linearize this exponential relationship, making the resulting absorbance value directly proportional to the concentration. This transformation ensures that a doubling of the light-blocking material doubles the absorbance reading, which greatly simplifies data interpretation.
Why Absorbance is the Preferred Metric
Scientists prefer absorbance because of its direct and linear relationship to the concentration of the substance being analyzed. This linearity is the central tenet of the Beer-Lambert Law, which states that absorbance is directly proportional to both the concentration (c) of the absorbing species and the path length (l) of the light through the sample. The equation A = \(\epsilon\)cl shows this relationship, where \(\epsilon\) is the molar absorptivity, a constant for a given substance at a specific wavelength.
The linearity between absorbance and concentration allows researchers to easily create a standard curve by measuring the absorbance of solutions with known concentrations. Once this curve is established, the concentration of any unknown sample can be quickly determined by measuring its absorbance. Conversely, transmittance has an exponential, non-linear relationship with concentration, meaning that plotting %T against concentration yields a curve rather than a straight line.
The non-linear nature of transmittance makes it less convenient for quantitative analysis. A small change in concentration does not correspond to the same change in %T across the scale. Converting the non-linear transmittance data into the linear absorbance metric is a fundamental step that transforms raw measurement into a quantifiable scientific tool. This makes absorbance the standard for determining concentrations in fields like biochemistry, clinical chemistry, and environmental monitoring.