a technical question about aperture openings

I remember hearing that the f-stop number is a mathematical value derived from the lens diameter and something. Is this true?

If so, will the f/8 opening (or any opening) in the physically larger 70-200 f/2.8 be larger than the f/8 opening in its smaller cousin 70-200 f/4?

It's a ratio between the aperture opening and lens length.

chuckmiller wrote in post #18914608
I remember hearing that the f-stop number is a mathematical value derived from the lens diameter and something. Is this true?

If so, will the f/8 opening (or any opening) in the physically larger 70-200 f/2.8 be larger than the f/8 opening in its smaller cousin 70-200 f/4?

As an f-stop is the ratio between the focal length of a lens to the diameter of the aperture, in a perfect world, two 200mm lenses set to f/8 should have the same aperture size no matter what the largest aperture size is. The reality is a bit more complicated than that.

To be precise, it is the ratio of the focal length of the lens system to the *apparent* diameter of the aperture as viewed from the front of the lens near infinity.

The actual physical aperture stop (i.e. what you get when you disassemble the lens like LensRentals) is smaller.

I mounted each lens, stopped it down to f/8, set the FL to 70mm, and looked inside. The aperture openinng looked pretty much identical. So, the physical size of the lens does not seem to matter, in this case.