朗伯-比尔定律Beer–Lambert law

透光率 T = I/I₀，吸光度 A = −lg T = lg(I₀/I)。光每通过一薄层，强度按比例减弱，积分后得到指数衰减 I = I₀·10^(−εbc)。ε 为摩尔吸光系数（L·mol⁻¹·cm⁻¹），是物质在特定波长下的特征常数，ε 越大测定越灵敏：ε > 10⁴ 为强吸收（如共轭体系 π→π* 跃迁），ε < 10² 为弱吸收（如 n→π*、d-d 跃迁）。吸光度具有加和性：多组分体系总吸光度等于各组分吸光度之和。

Transmittance T = I/I₀ and absorbance A = −log T = log(I₀/I). Each thin layer removes a fixed fraction of the light, so integration gives exponential decay, I = I₀·10^(−εbc). The molar absorptivity ε, in L·mol⁻¹·cm⁻¹, is characteristic of the substance at that wavelength; the larger ε, the more sensitive the measurement: above 10⁴ is strong absorption (such as π→π* in conjugated systems) and below 10² weak (n→π*, d–d transitions). Absorbances are additive, so a mixture's total absorbance is the sum of its components'.

1729 年法国的布格尔发现光强随吸收层厚度呈指数衰减；1760 年德国的朗伯用数学形式表述了这一关系；1852 年德国的奥古斯特·比尔发现吸光度与溶液浓度成正比。三者结合即为现在的朗伯-比尔定律（也称布格尔-朗伯-比尔定律）。

In 1729 Bouguer in France found that light intensity decays exponentially with the thickness of an absorbing layer; Lambert in Germany put this in mathematical form in 1760; and in 1852 August Beer in Germany found absorbance proportional to concentration. Together these give the Beer–Lambert (or Beer–Lambert–Bouguer) law.

定律只在以下条件下严格成立：单色光、稀溶液（通常 < 0.01 mol/L，浓溶液中分子相互作用改变 ε）、吸光物质不发生解离、缔合或化学反应、溶液均匀无散射。仪器方面的杂散光和多色光会使高浓度时标准曲线向下弯曲。实际测定时吸光度控制在 0.2–0.8 范围内相对误差最小。

The law holds strictly only for monochromatic light, dilute solutions (usually below 0.01 mol/L, since interactions change ε at higher concentration), absorbers that do not dissociate, associate or react, and homogeneous, non-scattering solutions. Stray light and polychromatic light make calibration curves bend downward at high concentration. Relative error is smallest with absorbances between about 0.2 and 0.8.