= Lambert's cosine law
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{title2=$I(\theta)=I(0)\cos\theta$}
{wiki}
For an ideal diffuse emitting or reflecting planar surface with uniform direction-independent <radiance>, the <radiant intensity> in a direction at <angle> $\theta$ to its <unit normal> is $I(\theta)=I(0)\cos\theta$. This follows immediately from $I=LA\cos\theta$ and the <projected area> formula. The worked <radiance> example and diagram show the $0^\circ$ and $60^\circ$ cases. <Lambertian reflectance> supplies one physical idealization realizing the law; an ideal <blackbody> provides an emitting example.
The historical setting is Johann Heinrich Lambert's \i[Photometria sive de mensura et gradibus luminis, colorum et umbrae], published in Augsburg in 1760. Its Part I, §139, explicitly compares normal and oblique illumination using the sine of the source's elevation, equivalently the <cosine> of its <angle> from the receiving <normal vector>. This is an early receiving-surface projection calculation; the modern outgoing-patch statement above keeps <radiance>, <radiant intensity> and <irradiance> distinct. https://www.e-rara.ch/zut/content/titleinfo/2814923[Lambert, Photometria, 1760, digitized original held by ETH-Bibliothek Zürich]{ref} https://www.e-rara.ch/zut/download/ftpack/plain/2814923[Photometria, searchable text, Part I, §139]{ref}.
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