04 // Interactive Formula Compendium // CHEMISTRY-THERMOA = ε · l · c = −log₁₀(I / I₀)
Beer-Lambert Optical Absorbance Law
The Beer-Lambert law A = εlc relates dimensionless absorbance A = −log₁₀(I/I₀) linearly to molar extinction coefficient ε (L·mol⁻¹·cm⁻¹), optical path length l (cm), and solute concentration c (mol/L).
Formula Reference
Main Formula
A = ε · l · c = −log₁₀(I / I₀)
Rearranged Forms
T = I / I₀ = 10^(−A)
c = A / (ε · l)
Variables & Units
| Symbol | Name | Unit |
|---|---|---|
| A | Optical Absorbance A | AU |
| eps | Molar Absorptivity ε | L/(mol·cm) |
| l | Cuvette Path Length l | cm |
| c | Molar Concentration c | mol/L |
Inputs & Parameters
[L/(mol·cm)]
[cm]
[mol/L]
Calculated Result (Optical Absorbance A)
A =0.622AU
Formula Notes & Background
- Differential attenuation dI = −σ N I dx integrated across thickness l yields I = I₀ e^(−σNl), converted to base-10 absorbance A = εlc.
- Spectrophotometers are most accurate for A between 0.1 and 1.5 AU (transmittance 79% down to 3.2%).
Step-by-Step Examples
#1: NADH solution at c = 1.0 × 10⁻⁴ M (100 μM) measured at 340 nm (ε = 6,220 M⁻¹cm⁻¹) in a standard 1.0 cm quartz cuvette.
ε = 6,220 L/(mol·cm)l = 1.0 cmc = 1.0×10⁻⁴ M
A = 6,220 × 1.0 × 0.0001
→ A = 0.622 AU (Transmittance T = 10^(−0.622) = 23.9%)
#2: DNA concentration check at 260 nm where A = 1.00 corresponds to 50 μg/mL dsDNA in a 1 cm path.
Measured A₂₆₀ = 0.48 AUl = 1.0 cm
Concentration = 0.48 × 50 μg/mL
→ 24.0 μg/mL dsDNA
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Frequently Asked Questions
Why does Beer-Lambert linearity deviate above A > 2.0?+
At A = 2.0 only 1% of light transmits (0.1% at A = 3.0), so stray instrument light, refractive index shifts, and solute dimerization cause apparent flattening.
What does A = 1.0 mean in terms of transmitted light?+
A = 1.0 means 90% of incident photons are absorbed and exactly 10% are transmitted (I/I₀ = 0.10).
Why are UV measurements below 300 nm run in quartz rather than plastic/glass cuvettes?+
Standard borosilicate glass and polystyrene strongly absorb UV wavelengths below 320 nm, whereas fused quartz is transparent down to 190 nm.