In article <4e67kr$4mg@mark.ucdavis.edu>, garydo@saturn.ece.ucdavis.edu says...

I have seen and read a lot of articles in this newsgroup and yet
could not come across one that explains what the aperture number (as
seen on the lens barrel) really means. How do they come up with those
numbers and why is it not linearly scaled? Also, on subject that
requires slight amount of exposure correction such as +1/3 EV, how
does one compensate for that using the aperture ring of the lens?

The focal-length of the lens (distance from the optical center of the
lens [at infinity focus] to the film) divided by the diaphram size
equals the f number - i.e., 100mm/25mm = f4; 50mm/25mm = f2;
50mm/12.5mm = f4; etc. (From this you can see why the numbers double
every two stops [the diameter of the aperture is halved {or doubled},
so the area is quartered {or quadrupled}, producing the 1/2 x 1/2 =
1/4 {or 2 x 2 = 4} double halving {or double doubling} of the diaphram
area for the two stop light change {a one stop change halves or doubles the amount of light going through the lens}]. The whole stops inbetween are at a ratio of 1 to the square root of 2 [since, to halve or double the area of the diaphram, the radius must be divided or multiplied by the square root of 2], resulting in the f stop sequence: f.7, f1, f1.4, f2, f2.8, f4, f5.6, f8, f11, f16, f22, f32, f45, f64, f90, f128, f180, f256, etc.). If you want to change the exposure by 1/3
stop (or 1/4, or 1/2, etc.) using the aperature ring, move it in the
desired direction by the same proportion as the f stop change you want
to make. BTW, this is why some of us prefer that only the whole stops
on the aperture ring have click positions - it makes it easier to
select a range of fractional stop settings.
Hope This Helps