Book: Photometria

Overview
Photometria, published in 1760 by Johann Heinrich Lambert, is the founding treatise of quantitative light measurement. It lays out a systematic theory connecting geometry, experiment, and mathematical analysis to describe how light illuminates surfaces, is reflected, transmitted, and absorbed. The work established photometry as a distinct scientific discipline and supplied precise laws and definitions that have persisted in optics and related fields.
Photometria combines careful experiments with rigorous derivations, moving beyond qualitative descriptions of brightness to measurable relationships between sources, media, and illuminated surfaces. Lambert's approach treated light as a measurable physical quantity susceptible to the same mathematical scrutiny applied in mechanics and astronomy, which allowed practical comparison of luminous sources and the prediction of illumination in complex geometries.

Central concepts and laws
One of the clearest legacies of Photometria is the formulation of what is now called Lambert's cosine law: the observed intensity from an ideal diffusely reflecting surface varies in proportion to the cosine of the angle between the surface normal and the direction of observation or illumination. This simple geometric rule explains why a surface appears dimmer when viewed at a grazing angle and underpins modern understanding of diffuse reflection and radiance.
Lambert also treated the diminution of light with distance for localized sources, affirming the inverse-square character of illumination from point-like emitters when radiation spreads uniformly over a spherical surface. In addition, he described the attenuation of light through absorbing media, establishing the proportional relationship between optical thickness and logarithmic reduction of intensity that later became part of the Beer–Lambert framework for absorption in materials.

Methods and experiments
The book details practical photometric methods for comparing luminous intensities and measuring the brightness of surfaces. Lambert designed and used comparative photometers, apertures, and controlled geometries to reduce subjective judgment and to quantify contrast between sources and reflected patches. He combined careful measurement with analytic geometry and infinitesimal calculus to derive integral expressions for illumination produced by extended sources and by surfaces with varying reflectance.
Experiments described in Photometria cover reflection and transmission, scattering by surfaces of different finishes, and the influence of intervening media. Lambert's insistence on reproducible procedures and his use of mathematical models to interpret data set a new standard for experimental optics, enabling others to convert observational facts into predictive formulae.

Influence and legacy
Photometria's influence reaches broad areas of science and engineering: optical theory, astronomical photometry, atmospheric optics, lighting engineering, remote sensing, and computer graphics. The concepts of a Lambertian surface and the cosine law remain central to models of diffuse reflection and radiative transfer. The book's treatment of absorption laid groundwork for later chemical and spectroscopic formulations relating concentration, path length, and attenuation.
Beyond particular laws and formulas, the enduring value of Photometria lies in its synthesis of experiment, geometry, and calculus to tame a complex phenomenon. Lambert's insistence that light can be quantified and predicted transformed how scientists measure illumination and reflectance, and that change shaped both practical technology for measuring light and theoretical developments in the physics of radiation.