That concept, you can't increase the radiance or photometric units,

the brightness of a light source, is so important.

Let's derive it again in a very,

very simple fashion in a way that we

referred to a number of times already through the course.

Let's say I am imaging an extended source over here to some detector or other plane.

So, in between these two planes I have a magical optical system,

one of my black boxes.

So my initial source has a certain amount of power phi,

it radiates out of a certain area A and into a certain solid angle omega,

and I shove that into the entrance pupil of my optical system.

It then comes back out the exit pupil somewhere else,

and it may have a new solid angle omega prime and a new angle,

our new area A prime.

Perhaps the system isn't 100% efficient,

its transmission may be perfect.

That's of course formally impossible but it's the upper limit.

So, there's some efficiency or transmission T output here.

The definition of T really is,

if the optical system were perfect,

the amount of power that would come out

phi prime is down by a factor of T from the amount of power that went in.

Well, conveniently now we can plug in for

these powers the definition of the radiance of this plane,

so phi prime is L prime A prime omega prime.

That's easy and I'll do the same thing over here.

That's just the definition of the radiance off of both sources.

Well, now let's use the fact that we know something about

how the area going in relates to the area coming out.

It's bigger by a factor of the magnification.

And we also know something about the solid angles going out given a solid angle going in.

It's down by a factor of the same magnification.

In other words, this is the angular magnification which is one

over m. And as we've said multiple times before,

the M's cancel and therefore sort of the areas and

the solid angles and we find that the radiance coming out is the radiance going in,

at worst, down by some overall transmission,

at best, T equals 1 and the radiance is conserved.

You cannot increase the radiance through an optical system.

That's really important and it's

fundamental to how light propagates and the sheet of light,

it's not something you can do better on.

So, when you push light through optical systems,

this law and the various details we've had before,

has to be foremost in your mind.