Beer-Lambert Law

Optical Absorption

When light passes through a solution, molecules absorb photons at characteristic wavelengths. The Beer-Lambert Law relates absorbance to concentration:

$A = \varepsilon \cdot c \cdot l$

Where:

• A — absorbance (dimensionless, also called optical density OD)
• ε — molar extinction coefficient (M⁻¹·cm⁻¹)
• c — molar concentration (mol/L = M)
• l — path length (cm); cuvettes are typically 1 cm

Transmittance

Transmittance T is the fraction of light that passes through:

$T = \frac{I}{I_0} = 10^{-A}$

Therefore: A = −log₁₀(T)

Common Extinction Coefficients

Protein Concentration (A280)

Proteins absorb at 280 nm due to Trp and Tyr residues. Using a protein-specific ε:

$c_{\text{mg/mL}} = \frac{A_{280}}{\varepsilon_{\text{mg/mL}}}$

DNA Concentration (A260)

Double-stranded DNA: 1 A260 unit ≈ 50 μg/mL. Single-stranded DNA: 1 A260 unit ≈ 33 μg/mL.

The A260/A280 ratio indicates purity: pure DNA ≈ 1.8, pure RNA ≈ 2.0.

Functions to Implement

• absorbance(epsilon_M_cm, c_M, l_cm=1) — compute A = ε·c·l
• transmittance(A) — compute T = 10^(−A)
• concentration_from_absorbance(A, epsilon_M_cm, l_cm=1) — solve for c
• absorbance_from_transmittance(T) — compute A = −log₁₀(T)