focal length - Does focus breathing make a lens slower when close focusing?

I've heard that focal length of some lenses will become noticeably longer when focusing to a close distance, an effect called "focus breathing". Since f-number is focal length divided by diameter of physical aperture and aperture size does not change, it seems logical to conclude that such lens should become slower when focusing close.

Is that really so, or is there something I'm overlooking?

Answer

That is true, and very noticeable in macro lenses. For example a Nikon 105mm f/2.8 VR (at infinity) is f/4.8 at it's closest focus distance of 30cm or so.