Question

Determine the luminosity of a surface whose luminance depends on direction as `L = L_(0) cos theta`, where `theta` is the angle between the radiation direction and the normal to the surface.

Answer 1

Luminance `L` is the light energy emitted per unit area o fthe emitting surface in a given direction per unit solid angle divided by `cos theta`. Luminosity `M` is simply enegry emitted per unit area.
Thus `M = int L. cos theta. dOmega`
where the integration must be in the forward hemisphere of the emitting surface (assuming light is being emitted in only one direction say outward direction of the surface) But
`L = L_(0) cos theta`
Thus `M = int L_(0) cos^(2) theta.d Omega = 2pi int_(0)^(pi//2) L_(0) cos^(2) theta sin theta d theta = (2)/(3) pi L_(0)`