Lambert's Law

A law according to which the luminance L of a light-scattering (diffusing) surface is the same in all directions; formulated in 1760 by J. Lambert. Today this law is considered to be a model of idealized diffusion of light, convenient for theoretical studies.

It follows from Lambert’s law that there is a constant relation between the luminosity M and luminance: M =π L. It also follows that the luminous intensity radiated by the plane scattering area Δ5 in any direction depends on the angle α between the direction and a line perpendicular to ΔS: I_α = I ₀ cos α.

This expression signifies that the luminous intensity of a plane surface is a maximum (I₀) along the perpendicular to that surface and, decreasing with increasing a, becomes equal to zero in a direction tangential to the surface.

In reality, only a few real bodies diffuse light without major deviations from Lambert’s law, even within the visible spectrum. Among such bodies are the dull surfaces of gypsum, magnesium oxide, and barium sulfate; some types of clouds and of milky glass among turbid media; and ideal black bodies and powdery luminophors among luminescent emitters. Nevertheless, Lambert’s law finds application not only in theoretical works but also for approximate photometric and illumination calculations.