The workhorse of the spectrophotometry lab: A = ε·b·c. Absorbance rises in step with concentration, and transmittance follows T = 10−A. Set the concentration, path length and molar absorptivity to read A and %T live — then dial in stray light and a polychromatic beam to see exactly why a real calibration curve bends away from the straight Beer's-law line at high absorbance.
Drag across the plot to set concentration. Dashed = ideal Beer's law; solid = measured.
Absorbance A—
Transmittance %T—
Ideal A (Beer's law)—
Deviation (Aideal − A)—
Absorbance is linear in concentration — transmittance is not. Beer's law A = ε·b·c is a straight line, so doubling the concentration doubles A. But because T = 10−A, the light actually reaching the detector falls off logarithmically: A = 1 lets 10% through, A = 2 only 1%. That is why quantitative work is done in absorbance, and why the useful range tops out near A ≈ 1–1.5 — beyond it, stray light and a finite spectral bandwidth bend the calibration curve below the ideal line.
How It Works
One straight line, one logarithm, and the two reasons real instruments stray from it.
1
A = ε·b·c
Each layer of solution removes the same fraction of the light, so absorbance adds up in proportion to how much analyte the beam meets: the molar absorptivity ε (how strongly it absorbs), the path length b the light travels, and the concentration c. Change any one and the ideal absorbance scales with it — that is the dashed line on the plot.
2
From absorbance to %T
What a detector measures is transmittance, T = I/I₀ = 10−A. The cuvette on the left darkens as concentration climbs and the transmitted beam dims to match. A rises without limit in theory, but %T is squeezed toward zero — by A = 2 only 1% of the light survives, so noise starts to dominate.
3
Why the real curve bends
Push Stray light up and a fixed slice of light skips the sample, capping absorbance at a ceiling. Push Polychromatic beam up and the band contains wavelengths of different ε; because the detector averages transmittance, not absorbance, the measured value lags the ideal. Both pull the solid curve below the straight line at high concentration — the classic negative deviation from Beer's law.
What is the Beer–Lambert law?
A = ε·b·c: absorbance is proportional to concentration, with ε the molar absorptivity (L·mol⁻¹·cm⁻¹), b the path length (cm) and c the concentration (mol/L). Absorbance and transmittance are linked by A = −log₁₀(T), so T = 10−A — A = 1 transmits 10% of the light, A = 2 only 1%. Because A is linear in c, absorbance vs concentration is ideally a straight line through the origin, which is what makes spectrophotometric calibration possible.
How do you calculate concentration from absorbance?
Rearrange to c = A / (ε·b). Measure the unknown's absorbance A, use the known ε for that analyte and wavelength and the cuvette path length b (usually 1 cm). Example: A = 0.400 with ε = 10,000 L·mol⁻¹·cm⁻¹ and b = 1 cm gives c = 4.0 × 10⁻⁵ mol/L (40 µmol/L). In the lab you read the unknown off a calibration curve of standards, which also absorbs small instrumental deviations.
Why do calibration curves deviate from Beer's law at high concentration?
Mostly for instrumental reasons, and always in the negative direction (below the line). Polychromatic light: the beam is a band of wavelengths with slightly different ε, and since the detector averages transmittance rather than absorbance, the measured A falls short. Stray light: a small fraction of light bypasses the sample, setting a ceiling A can't exceed. Chemical effects (association/dissociation, pH, refractive-index changes) add more. This tool demonstrates the two instrumental causes.
What is molar absorptivity (ε)?
It measures how strongly a substance absorbs at a given wavelength, in L·mol⁻¹·cm⁻¹ — effectively the slope of the Beer's-law line per unit path length. A large ε means a strongly coloured, sensitive analyte reaching high absorbance at low concentration; a small ε needs more path or concentration for the same A. ε depends on the substance and wavelength, so measurements are taken at the absorbance maximum, λmax.
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