It's probably nice to have some measure of how big this is.

And the common measure is to go from the center to the first null.

That's arbitrary.

You could go center to half way down the peak, full width, half max,

or half width half max.

The Gaussian beam, we want the radius of the 1 over e point

of the field, because it was convenient.

The point is, there's a little bit of ambiguity here in

how big is this function, that's dependent on how you choose to measure it.

And you should hope be sure you know what that measure is.

But for a function that's got nulls,

as this one does, it's really common to measure the radius to the first null.

Well, that's really easy.

We set this function right here equal to pi.

And that tells us where that r naught is, that first radius, coordinate x prime.

And that's simply FD over lambda.

That bit right there.

We'll notice focal length over diameter is a quantity we've already run into.

That's called the F number of this lens.

Or we've also run into this and described it as numerical aperture.

That's just basically the diameter, sorry, radius of the lens, over the focal length.

So in the paraxial approximation, it's this angle right there.

Or, the sine of it in the non-paraxial approximation.

So, both of these expressions are really useful to remember.

The spot size measures radius to first null is F number times lambda.

This is why F number is an important and useful quantity.

It tells you the resolving power.

The size of your focal spot given in units of the wavelength.

So if you have an F1 lens, it's a powerful well corrective lens,

it's tiny foci that decides the wavelength.

If you have an F10 lens, your spots in radius to first null are 10 wavelengths.