A unified electromagnetic framework for light absorption: beyond the Bouguer–Beer–Lambert law

The Bouguer–Beer–Lambert law is undoubtedly the most important law in spectroscopy, being indispensable for chemical analysis and quantitative measurements. Its straightforward formulation and elegant functionality have attracted wide applicability across diverse scientific disciplines and industries. However, fundamental, chemical and instrumental deviations exist mostly stemming from the inherent formulating assumptions of the law have limited its usefulness and effectiveness. Consequently, this has sparked an enthusiastic pursuit of modifications aimed at enhancing precision and extending its capabilities. Modifications based on classical theories have fallen short in addressing, specifically, the fundamental deviations where at high concentrations, the intermolecular interactions become prevalent. Electromagnetism resolves these shortcomings by providing a detailed description of molecular-scale light-matter interactions incorporating effects of polarizability, electric displacement and refractive index. This study thus formulates an extension of the Bouguer–Beer–Lambert law based on electromagnetic theory to solve the problem of real or fundamental deviations. The modified Bouguer–Beer–Lambert model was evaluated in both organic and inorganic solutions using potassium permanganate (VII), potassium dichromate (VI), methyl orange, copper (II) sulfate and iron (III) chloride. The proposed modification demonstrated outstanding performance, achieving a root mean square error (RMSE) of less than 0.06 for all tested materials and displaying remarkable capabilities far beyond the Bouguer–Beer–Lambert law. The unparalleled accuracy and practical simplicity of the unified modified model make it a valuable and exceptional enhancement of the existing Bouguer–Beer–Lambert law, paving the way for accurate absorption measurements across diverse fields.