Question on Radiance equation

Question

The radiance equation is $$ L = \frac{d}{dA} \frac{2(\phi)}{dW cos(\theta)} (watt/srm^2) $$ where $\phi$ is the flux.

I am thinking, should not be the cosine term on the numerator instead of the denominator? Having the cosine in the denominator will make L goes to infinity if $\theta = 90$ , which does not make sense to me. My understanding is that if $\theta = 90$ (i.e. flux direction is perpendicular to the surface normal), then $L$ should equal to zero (and not infinity).

Answer 1

The formula correctly reflects the definition of radiance, so it's certainly correct in this sense. Is such a definition useful? I guess so - the value defined in this way gives some idea of "brightness" of the source, and "brightness" does tend to infinity when the angle tends to 90 deg - the same flux comes from a very small "perceived" area.