ok things are getting clearer
NOW I understand the cosine law ...
can you help my thought experiment along
point light with intensity I
surface element subtends solid angle O
incident flux is F = I * O
surface element has surface area A
irradiance is E = F / A
reflectance is 100%
so emittance M = E
and radiance is ... now I am stuck
I could say the radiance is also M
as we have already divided by an area and by a solid angle ...
but we haven't taken into account the diffuse scattering
Or I could say that radiance is M / pi
which accounts for the scattering, but is now an average over the hemisphere
now I can see how to calculate the flux entering an eye's pupil
(integrate solid angle subtended by pupil and surface area of surface)
but then projected area pops up ...