All matter interacts with light in one of three fundamental ways: it can be reflected, absorbed, or passed through. Understanding how much light is transmitted through a material or a solution is a foundational concept in many scientific disciplines. By precisely measuring these light-matter interactions, scientists gain deep insights into a material’s physical and chemical properties. Quantifying these optical properties allows for the determination of a substance’s identity, purity, and most importantly, its concentration in a solution.
Defining Transmittance and Its Calculation
Transmittance (\(T\)) is a precise physical quantity that describes the fraction of incident light that successfully passes through a sample without being absorbed or scattered. It is a ratio comparing the intensity of the light exiting the sample (\(I\)) to the initial incident light intensity (\(I_0\)). This is expressed by the formula \(T = I/I_0\).
Because \(T\) is a simple ratio, its value always falls between zero and one. A transmittance of 1.0 means 100% of the light passed through, indicating no absorption. Conversely, a transmittance of 0.0 means no light passed through, signifying complete absorption by the sample.
Scientists frequently express this value as a percentage, known as percent transmittance (\(\%T\)), calculated by multiplying the ratio by 100. This provides a straightforward, intuitive way to describe how transparent a substance is at a specific wavelength.
Measuring Light Passage with Spectrophotometry
The practical measurement of transmittance is accomplished using a specialized instrument known as a spectrophotometer, which analyzes light intensity across a range of wavelengths. The process begins with a light source that emits a broad spectrum of radiation. This light is directed through a monochromator, which isolates a very narrow band of light.
This purified, monochromatic light beam, representing the incident intensity (\(I_0\)), is then passed through the sample contained within a cuvette. As the light travels through the sample, some photons are absorbed by the molecules in the solution, reducing the intensity of the beam. The remaining light, the transmitted intensity (\(I\)), then strikes a detector.
The detector converts the light energy it receives into an electrical signal proportional to the intensity of the transmitted light. The instrument’s internal software calculates the transmittance by comparing \(I\) to \(I_0\). This precise comparison reveals how much of the original light was able to pass through the sample at the selected wavelength.
The Essential Link to Sample Concentration
While transmittance provides a direct measure of light passage, it has an inverse and non-linear relationship with the concentration of the substance being analyzed. As the concentration of a colored solution increases, the amount of light transmitted decreases exponentially, making it challenging to directly correlate the two values. For this reason, scientists convert transmittance into a different metric called absorbance (\(A\)).
Absorbance is the preferred measurement because it maintains a straightforward, linear relationship with a sample’s concentration. The conversion between the two is defined by an inverse logarithmic relationship: \(A = -\log_{10}(T)\). For instance, \(100\%\) transmittance corresponds to an absorbance of \(0\), while \(10\%\) transmittance corresponds to an absorbance of \(1.0\).
This linear relationship is formally described by the Beer-Lambert Law, which states that the absorbance of a solution is directly proportional to both the concentration of the light-absorbing substance and the distance the light travels through the solution.
By measuring the transmittance, and subsequently calculating the absorbance, scientists can create a calibration curve using solutions of known concentrations. This graph plots absorbance against concentration, resulting in a straight line that can be used to determine the concentration of any unknown sample.
This capability makes transmittance measurement a fundamental technique in analytical science. It is routinely used in clinical laboratories to quantify the concentration of various substances in blood or urine, such as glucose or proteins. In environmental testing, it is used to determine the concentration of pollutants in water samples, providing a fast and accurate method for quantitative analysis.