i discovered that to get to the next f stop, u multiply by (make a guess?) yes! root 2! haha ^^
so the f numbers are 1, 1.4, 2, 2.8, 4, 5.6, 8, ...
it's a geometric progression with a common ratio of root 2.
why is that so nei?
borrowing from wiki, "In optics, the f-number (sometimes called focal ratio, f-ratio, or relative aperture[1]) of an optical system expresses the diameter of the entrance pupil in terms of the effective focal length of the lens; in simpler terms, the f-number is the focal length divided by the aperture diameter. It is a dimensionless number that is a quantitative measure of lens speed, an important concept in photography"
well, with each stop, the aperture area is HALVED... (see diagram, courtesy of wiki)
Let T(n) and D(n) be respectively the area and diameter of the nth circle. Let the radius of the nth circle be r.
Then,
T(n) = pi(r)^2, D(n) = 2r
T(n + 1) = (1/2)pi(r)^2 = pi[(1/root2)r]^2, D(n + 1) = 2(1/root2)r = root2(r)
so, D(n + 1)/D(n) = 1/root2
which means the diameters form a geometric progression with common ratio 1/root2 i.e. to get to the next diameter, u DIVIDE by root2.
but f/# and diameter have an inverse relationship so that's why, to get to the next f number you MULTIPLY by root 2!
Here are the typical one-half-stop n one-third-stop f-number scales. note that the numbers in bold form the geometric progression i mentioned above, with common ratio root 2.
Typical one-half-stop f-number scale
f/# 1.0 1.2 1.4 1.7 2 2.4 2.8 3.4 4 4.8 5.6 6.7 8 9.5 11 13 16 19 22
(courtesy of wiki)
Typical one-third-stop f-number scale
f/# 1.0 1.1 1.2 1.4 1.6 1.8 2 2.2 2.5 2.8 3.3 3.5 4 4.5 5.0 5.6 6.3 7 8 9 10 11 12.5 14 16 18 20 22
(courtesy of wiki)
omoshiroi ne! ^^
