Question: At first glance the cosine in the denominator of the equation for a perfect reflector BRDF might seem a little odd. Why is this the correct formula for the BRDF of a perfect reflector? (Hint: you may want to take a look at the next slide.)
If I shine a spotlight at wall at perpendicular, it makes a small circle. If I shine it at the same wall 1 degree off perpendicular, it makes a large ellipse. The ellipse has much more area, but power is conserved. Therefore the wall must be reflecting much less light per point.
If the wall is instead a mirror, we have perfect specular reflection instead of diffuse reflection. But the fact that we have the same amount of energy reflecting at more points doesn't change.