Measuring Brightness

Illuminance(E) = luminous flux(Ø) / area(A)

Luminous flux is the power output of a light source corrected for the dependence on wavelength of the sensitivity of the human eye, and it is measured in lumen, written as lm (Ø). Illuminance on a surface is the luminous flux per unit area falling on the surface (E). It is measured in lux, written as lx. 1 lx = 1 lm/m^(2).

Lambert's cosine law

Let the vertical surface be A, and the leaning surface be A'. Since A'=A/[cos(theta)], E' = Ø/A' = Ø/{A/[cos(theta)]} = (Ø/A)·cos(theta) = E•cos(theta).

when r doubles, E times1/4; when r triples, E times 1/9...

A spherical surface of radius r has an area of 4πr^2. If the luminous flux of the source is Ø, the illuminance on the surface will be E=Ø/(4πr^2).

light from a point source falls at an angle on a plane surface

Suppose point X on the surface is r away from the source, whose luminous flux is Ø, and the light hits the surface at an angle theta at X. By combining E'=E•cos(theta) and E=Ø/(4πr^2), the illuminance at X is given by E=Ø•cos(theta)/(4πr^2).

Luminous Efficacy=Ø/P

Luminous efficacy (or efficacy) measures the effectiveness of a light source, and is measured in lm/W.