Beer-Lambert Law
The Beer-Lambert Law explained — how light absorbance relates to concentration and path length.
Includes formula, variables, and spectrophotometry examples.
The Formula
The Beer-Lambert Law (also called Beer's Law) describes how light is absorbed as it travels through a solution. The absorbance A is directly proportional to both the concentration of the absorbing substance and the path length through the sample. It is the foundation of spectrophotometry — one of the most widely used analytical techniques in chemistry, biology, and medicine.
Variables
| Symbol | Meaning | Unit |
|---|---|---|
| A | Absorbance (dimensionless, log scale) | AU (absorbance units) |
| ε | Molar absorptivity (extinction coefficient) | L·mol⁻¹·cm⁻¹ |
| c | Concentration of the absorbing species | mol/L (M) |
| l | Path length (distance light travels through sample) | cm |
Transmittance and Absorbance
Where T = transmittance (fraction of light that passes through), I = transmitted intensity, I₀ = incident intensity. An absorbance of 1.0 means 90% of light is absorbed; A = 2.0 means 99% absorbed.
Example 1 — Finding Concentration
A protein solution is measured in a 1 cm cuvette. Absorbance A = 0.65, ε = 43,000 L·mol⁻¹·cm⁻¹
Rearrange: c = A / (ε × l) = 0.65 / (43,000 × 1)
c = 1.51 × 10⁻⁵ mol/L = 15.1 µM
Example 2 — Predicting Absorbance
A dye solution: c = 2.0 × 10⁻⁴ M, ε = 8,500 L·mol⁻¹·cm⁻¹, l = 2 cm
A = 8,500 × 2.0 × 10⁻⁴ × 2 = 8,500 × 0.0004
A = 3.4 → only 0.04% of light passes through (nearly opaque)
Calibration Curve
In practice, Beer's Law is validated by preparing a series of known concentrations and plotting A vs. c. A straight line through the origin confirms the law holds in that range. Deviations at high concentrations are common due to molecular interactions.
When to Use It
- Measuring protein and DNA concentrations in biochemistry labs
- Water quality testing — detecting pollutants and dye concentrations
- Medical diagnostics — glucose, haemoglobin, and enzyme assays
- Industrial quality control — checking dye consistency in textiles and paints
- Atmospheric science — modelling how gases absorb solar and infrared radiation
- Determining unknown concentrations from absorbance measurements