How this instrument works
The Beer-Lambert law describes how much light a solution absorbs as it passes through it: absorbance A grows in direct proportion to three things — how strongly the dissolved species absorbs light at a chosen wavelength (its molar extinction coefficient, ε), how much of it is dissolved (concentration, c), and how far the light has to travel through the solution (path length, l). Double any one of the three and absorbance doubles; the relationship is a straight multiplication, not a curve.
This linearity is what makes UV-vis spectrophotometry so useful for measuring concentration. A spectrophotometer reports absorbance directly, and if ε and l are known — ε is a property of the absorbing species at a given wavelength, and l is fixed by the cuvette, typically 1 cm — then the one remaining unknown, concentration, falls straight out of the rearranged formula. This is exactly how a lab quantifies an unknown protein, dye or drug concentration from a single absorbance reading, once it has calibrated ε for that species.
The law does have limits. It holds cleanly at low-to-moderate concentrations, but at high concentration the absorbing molecules start interacting with each other and with the solvent in ways the simple linear model doesn't capture, so measured absorbance bends away from the straight line the formula predicts. Chemists work around this by diluting a sample until its reading falls back into the law's linear range before trusting a concentration calculated from it.
- Enter the species' extinction coefficient at your chosen wavelength into Molar extinction coefficient, epsilon (L/(mol*cm)).
- Enter the solution's concentration in mol/L into Concentration (mol/L).
- Enter how far light travels through the sample into Path length (cm) — 1 cm is the standard cuvette width unless yours is stated otherwise.
- Read the predicted reading straight off Absorbance, A — a unitless number, since absorbance is a base-10 logarithm of a light-intensity ratio.
- If you're solving in the other direction — you measured A and want concentration — rearrange to c = A / (ε × l) using your known ε and l.
Worked example — a strong chromophore at 0.1 mM
Enter 15000 into Molar extinction coefficient, epsilon (L/(mol*cm)), 0.0001 into Concentration (mol/L), and 1 into Path length (cm) — a strong-chromophore extinction coefficient, a 0.1 millimolar solution, and a standard 1 cm cuvette. Absorbance, A reads 1.5000.
The arithmetic is a single multiplication: A = 15000 × 0.0001 × 1 = 1.5 exactly. An absorbance of 1.5 means the solution transmits only about 3% of the incident light at that wavelength (10⁻¹·⁵ ≈ 0.0316) — well within the range most spectrophotometers measure reliably, and a reading a chemist could use with confidence to back-calculate concentration if ε were the unknown instead.
Questions
What does an absorbance of 1.5 actually mean?
Absorbance is a base-10 logarithm of how much light gets through: A = −log₁₀(I/I₀), where I₀ is the light entering the sample and I is what makes it out the other side. An absorbance of 1.5 means only about 3% of the light transmits (10⁻¹·⁵ ≈ 0.0316), because each whole unit of absorbance corresponds to a tenfold drop in transmitted light.
Why is the molar extinction coefficient different for every substance?
Because it reflects how strongly a particular molecule's electronic structure interacts with light at a specific wavelength — a property fixed by that molecule's chemistry, not something you choose. Different compounds absorb most strongly at different wavelengths, which is why a lab first has to identify or look up the right ε for the species and wavelength it's actually measuring before trusting a concentration derived from A.
Why does absorbance stop being proportional to concentration at high concentrations?
The Beer-Lambert law assumes each absorbing molecule acts independently, but at high concentration molecules start interacting with each other and with the solvent — through effects like aggregation or changes in the local refractive index — that the simple linear model doesn't account for. The practical fix is diluting the sample until its absorbance falls back into a range (commonly cited as roughly 0.1 to 1.0) where the law holds cleanly.
Can I use this to find concentration if I already measured absorbance?
Yes — rearrange the same formula to c = A / (ε × l). Enter your measured A, and if you know ε for your species at your wavelength and the path length of your cuvette, you can solve for the unknown concentration by hand; this instrument computes A forward from ε, c and l, so run the arithmetic in reverse using your measured absorbance.
Does path length have to be 1 cm?
No — 1 cm is simply the most common standard cuvette width, chosen because it makes the arithmetic and reported ε values convenient to compare across labs. Some instruments use shorter or longer path lengths (microcuvettes, flow cells), and the formula works identically with any path length in centimetres, as long as ε is quoted in the matching L/(mol·cm) units.