Intensity of Illumination
The intensity of illumination is defined as the flux per unit area incident on a given surface, the ray falling perpendicular to the surface.
Consider a point source of light S and an element AB of surface area a that subtends a solid angle ω at the point S.
A flux of F lumens falls on the area AB. Intensity on AB = I = F/a
L is the illuminating power or luminous intensity of the source and it is defined as luminous flux per unit solid angle. Its unit is candela.
L = F/ω or, F = Lω
∴ I = Lω/a
Let the area AC be a1. But a1 = a cos θ
This is known as Lambert’s cosine law i.e. the intensity of illumination is directly proportional to the cosine of the angle of incidence of light radiations on the given surface.
To conclude, the intensity of illumination is (i) directly proportional to the illuminating power or luminous intensity of the source (ii) directly proportional to the cosine of the angle of incidence and (iii) inversely proportional to the square of the distance between the source and the surface.
Special case: if θ = 0, i.e. if the angle of incidence is zero, the surface is normal to the incident radiations and cos 0 = 1
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