So when you meet an optical system that you've never been introduced to before,

it turns out there's a very mechanical set of things you want to do

to understand these finite apertures.

And, principally, it involves tracing two particular rays.

And, these rays are very equivalent

to the two rays we use to understand Gaussian beams,

which was one of the other reasons I like that two ray mechanism for Gaussian beams.

So let's figure out what those are.

The first one is the marginal ray.

We're going to start at the object.

And you can tell this is my object right here because I have in light gray,

my little single headed arrow.

And I'm going to start a ray off of the axis.

So this would be like my divergence ray from the Gaussian beam language.

So it's going to start at the intersection of the object.

It depends on where the object is then.

And I think of this as just tilting this ray up.

I always hear a little mechanical sound in my head [SOUND] as I tilt this ray up.

And I would tilt this ray up.

And as I'm doing that, I'm tracing all the way through the optical system.

And we've done a simple one here.

But if I had 38 lenses and all sorts of stops distributed through this system,

I would trace this ray initially right down the axis.

So it obviously would get through the system.

And that I would keep increasing it until I hit

the first stop anywhere in the system that limited that ray.

And that is therefor the largest possible angle.

I'll call it alpha here.

That I can get off of the center of the object, and to my system.

That ray is really important.

It defines, just like the divergence ray for

the a Gaussian beam, the numerical aperture of the system.

And we've seen from the previous module, a numerical aperture is a hugely important

concept, and quantity about an optical system.