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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’s word has found its way into European languages as photometry, photometrie, and fotometria. Photometria was the first work to accurately identify most fundamental photometric concepts, assemble them into a coherent system of photometric quantities, define these quantities with a precision sufficient for mathematical statements, and ...
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 term ((^)) is needed on account of Lambert's law. [15] Mathematically, the quantity (,;) is not a vector because it is a positive scalar-valued function of the prescribed direction and sense, in this example, of the downward vertical. In this example, when the collected radiation is propagating in the downward sense, the detector is said to ...
Radiant intensity is used to characterize the emission of radiation by an antenna: [2], = (), where E e is the irradiance of the antenna;; r is the distance from the antenna.; Unlike power density, radiant intensity does not depend on distance: because radiant intensity is defined as the power through a solid angle, the decreasing power density over distance due to the inverse-square law is ...