Focal length is the distance from the rear nodal point (often, but not always the surface of the rear element)l to the focal plane when focused at infinity. The f-number is the focal length divided by the diameter of the lens entry pupil (the absolute aperture...often, but not always the diameter of the diaphragm iris opening) and is always written as the fraction f/(number).
You are correct that if the absolute aperture remains the same and the focal length increases, the relative aperture (f-number) will increase proportionally. The concept of relative aperture is very useful in that it allows easy calculation of exposure value (EV) that can be applied for consistent exposure across lenses regardless of focal length. This incredibly helpful when using a hand-held meter to determine exposure settings.
Unfortunately, there are two problems:
- F-number only strictly applies when focused to infinity. At close distances the effective focal length may be much longer than that stamped on the side of the lens.
- The mechanical "stops" that determine the size of the absolute aperture on a traditional zoom lens with aperture ring are not typically coupled to reflect changes to focal length as the lens is zoomed
As a result, the amount of light actually striking the film or sensor may vary quite a bit as a lens is zoomed and as focus is changed from far to near. The latter is readily observed with a 1:1 macro lens pointed at a blank target. As the focus ring is racked from far to near the viewfinder image becomes progressively darker and the meter display reflects the dimming numerically. The same may be observed when moving to a longer focal length with a zoom lens.
Enter through-the-lens metering. That allows for seamless correction of both the focus and focal length issues...assuming you are using manual settings or aperture-priority automation. For shutter-priority or programmed automation with a zoom lens, the aperture control must "know" the current focal length or the lens must be designed to maintain constant relative aperture regardless of focal length*. The second approach is the more desirable, but requires larger glass elements and more complicated designs.
Steve
* Explaining how this is done requires more words than I am willing to donate this evening...