Archived posting to the Leica Users Group, 2008/12/13
[Author Prev] [Author Next] [Thread Prev] [Thread Next] [Author Index] [Topic Index] [Home] [Search]Howard, Figures can't lie, but----------etc! Jerry Howard Ritter wrote: > No, it actually is MORE than 1/2 stop, not less, and way more than 1/3 > stop. Remember, f/4 is already a full stop down from f/2.8, so the > jump from f/2.8 to f3.5, already well over halfway numerically, is way > more geometrically. > > Squaring the reciprocal of the f-ratio gives a number that is > proportional to the aperture's area. > A full stop is an areal ratio of 2, corresponding to a ratio between > f-ratios equal to the square root of 2. A half-stop is an areal ratio > of sqrt (2), about 1.4, corresponding to a ratio between f-ratios > equal to sqrt(sqrt( 2)), about 1.189. > > 2.8 x 1.189 = about 3.3. > 3.3 x 1.189 = about 3.9. > So 1/2 stop down from f/2.8 is about f/3.3, with another > equal-proportion areal step down to f4. > > One-third of a stop is an areal ratio of the cube root of 2 (for three > equal-proportion areal steps from one full stop to the next), > corresponding to a ratio between f-ratios equal to the cube root of > sqrt(2), or about 1.12. > > 2.8 x 1.12 = about 3.1. > 3.1 x 1.12 = about 3.47. > 3.47 x 1.12 = about 3.9. > So 1/3 of a stop down from 2.8 is about f/3.1, with two more > equal-proportion areal steps down to f4. > > So from f/2.8 to f3.5 is actually 2/3 stop. Unless you were talking > about going from f/4 to f/3.5, which is 1/3 stop. (If you turn it > around and take 4/1.12, you get 3.57. The numbers are rounded because > they're irrational except for the alternate full stops f/1, 2, 4, 8, > 16..., as well as approximated in order to give numbers ending in an > even digit or a 5.) > > --howard > >