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In optics, Lambert's cosine law says that the observed radiant intensity or luminous intensity from an ideal diffusely reflecting surface or ideal diffuse radiator is directly proportional to the cosine of the angle θ between the observer's line of sight and the surface normal; I = I 0 cos θ.
Diagram of Lambertian diffuse reflection. The black arrow shows incident radiance, and the red arrows show the reflected radiant intensity in each direction. When viewed from various angles, the reflected radiant intensity and the apparent area of the surface both vary with the cosine of the viewing angle, so the reflected radiance (intensity per unit area) is the same from all viewing angles.
Lambert began conducting photometric experiments in 1755 and by August 1757 had enough material to begin writing. [11] From the references in Photometria and the catalogue of his library auctioned after his death, it is clear that Lambert consulted the optical works of Isaac Newton, Pierre Bouguer, Leonhard Euler, Christiaan Huygens, Robert Smith, and Abraham Gotthelf Kästner. [12]
The rays represent luminous intensity, which varies according to Lambert's cosine law for an ideal diffuse reflector. Diffuse reflection is the reflection of light or other waves or particles from a surface such that a ray incident on the surface is scattered at many angles rather than at just one angle as in the case of specular reflection.
The reflections from these surfaces can only be described statistically, with the exact distribution of the reflected light depending on the microscopic structure of the material. Many diffuse reflectors are described or can be approximated by Lambert's cosine law, which describes surfaces that have equal luminance when viewed from any angle ...
The directional reflectance of a surface, denoted R Ω, is defined as [1] =,,, where . L e,Ω r is the radiance reflected by that surface;; L e,Ω i is the radiance received by that surface.
The curve which represents the response of the human eye to light is a defined standard function y (λ) or V(λ) established by the International Commission on Illumination (CIE, for Commission Internationale de l'Éclairage) and standardized in collaboration with the ISO.
Lambert's cosine law says that the amount of light decreases with the cosine of the angle between the normal of the surface and the line of sight. But as the apparent surface the observer sees decrease with the same law, the brightness of the source remains constant.