Light interaction with matter is a fundamental concept in many scientific disciplines, providing insights into a material’s composition and properties. When light passes through a substance, some of it may be absorbed, and some may pass through. Scientists quantify these interactions using measurements like transmittance and absorbance. This article explains their relationship and the conversion process.
Understanding Transmittance and Absorbance
Transmittance quantifies the fraction of incident light that successfully passes through a sample. It is often expressed as a percentage, indicating how much light emerges relative to the amount that entered. For instance, 100% transmittance means all light passed through, while 0% transmittance indicates no light passed through. This measurement offers a direct view of how transparent a substance is to light.
Absorbance, conversely, measures the amount of light absorbed by a sample. It is presented on a logarithmic scale, making it a dimensionless quantity. While both terms describe how light interacts with a material, absorbance provides a more convenient scale for quantifying the extent of light absorption, particularly because it relates linearly to the concentration of absorbing substances in many cases. The logarithmic scale and negative relationship ensure that as light absorption increases, transmittance decreases, allowing a wide range of values to be represented effectively.
The Conversion Formula
The mathematical relationship between transmittance (T) and absorbance (A) is defined by a specific formula. Absorbance is calculated as the negative logarithm (base 10) of the transmittance: A = -log₁₀(T). If transmittance is initially given as a percentage (%T), it must first be converted into its decimal fraction form before applying the formula. For example, a transmittance of 50% must be converted to 0.50 (50/100) for use in the equation.
Step-by-Step Conversion and Practical Examples
To convert transmittance to absorbance, first ensure the transmittance value is in its decimal form; if given as a percentage, divide it by 100. Then, apply the formula A = -log₁₀(T). For example, if a sample has 75% transmittance, convert it to 0.75. The absorbance is A = -log₁₀(0.75), which equals approximately 0.125.
Consider another example where a solution transmits 10% of the light. Converting this to a decimal yields 0.10. Calculating the absorbance gives A = -log₁₀(0.10), which results in an absorbance of 1.0. This shows that lower transmittance values correspond to higher absorbance values.
To convert absorbance back to transmittance, the formula is T = 10⁻ᴬ. For instance, an absorbance of 0.5 converts to T = 10⁻⁰.⁵, which is approximately 0.316, or 31.6% transmittance.
Applications of Absorbance
Absorbance is a widely used measurement in various scientific disciplines due to its direct relationship with the concentration of a substance. Its primary application is in the Beer-Lambert Law, which states that the absorbance of a solution is directly proportional to the concentration of the absorbing species and the path length of the light through the solution.
This law is expressed as A = εbc, where:
A is absorbance
ε (epsilon) is the molar absorptivity (a constant specific to the substance at a given wavelength)
b is the path length (typically the width of the sample container)
c is the concentration of the substance
This relationship makes absorbance an important tool in spectrophotometry, a technique used extensively in chemistry, biology, and environmental science. Spectrophotometers measure the amount of light absorbed by a sample at specific wavelengths, allowing scientists to quantify the concentration of various substances, such as DNA, proteins, or pollutants in water samples. Absorbance measurements also play a role in quality control, drug analysis, and studying reaction kinetics by monitoring changes in concentration over time.