How much light a solution swallows, written in one line: A = ε·c·l. Absorbance is linear in concentration and path length; transmittance T = 10−A is what the detector actually sees. Rendered, not quoted — the engine below computes the law live and a planted flaw is caught by the witness.
source Beer, A. (1852) Bestimmung der Absorption des rothen Lichts in farbigen Flüssigkeiten, Ann. Phys. Chem. 86, 78–88 · Bouguer (1729) Essai d'optique · Lambert (1760) Photometria no stable DOI — cited by author/title/year
A beam of intensity I₀ enters a cuvette. Each thin slab absorbs a fixed fraction, so intensity falls exponentially with depth — and the exponent is proportional to both concentration and path length.
ε molar absorptivity (L·mol⁻¹·cm⁻¹) · c concentration (mol/L) · l path (cm). Double c → double A. Exact by construction.
Light through solution — the neighbour to the-nernst (an ion concentration read as a voltage). Here concentration is read as swallowed light. Both are logarithms of a ratio: Nernst takes ln of an activity ratio; Beer-Lambert takes log₁₀ of a transmittance ratio.
Absorbance is additive, transmittance multiplicative — the property every spectrophotometer inverts to recover an unknown c.
Re-runs the round trip A → T → A live on the current engine state. Green while −log₁₀(10−A) = A holds; flips red the instant the Tamper (window 6) swaps the base to e.
Three knobs feed the law: molar absorptivity ε, concentration c, and path length l.
Live engine — pure functions absorbance, transmittance. No baked numbers.
The result the detector reports and the law the spectrophotometer inverts:
"Absorbance is always linear in c, so I can read any concentration off a straight line." No. Linearity is an idealisation. At high c the analyte's molecules interact, the refractive index shifts, and stray light & polychromatic beams flatten the curve. The straight line is a low-concentration limit — the wall the law does not cross.
"Transmittance adds when you stack cuvettes."
→ Transmittance multiplies (T₁·T₂); it is absorbance that adds (A₁+A₂). Window 0 & selfcheck verify both.
"T = e−A for a base-10 absorbance."
→ That is the Tamper. For a base-10 A the detector reads T = 10−A; using base e breaks the round trip by exactly 1/ln10 ≈ 0.4343.
"ε is a fixed material constant."
→ AMBER ε depends on wavelength, solvent and temperature; the law holds at a fixed λ.
Swap the transmittance base from 10 to e while still labelling A as base-10. The panel keeps running — but the round trip in window 7 no longer closes.
base = 10 (intact)