jeh@ritcv.UUCP (Jim Heliotis) (04/30/85)
What is the relationship between f-stops and stops? I think I know what it is
in shutter speeds:
delta(stops) = log2(old-speed / new-speed)
sort of like S/N ratios in bels.
Can anyone tell me the equivalent formula for f-stops? A description of
exactly how they are measured would be nice, too.
Jim Heliotis
{allegra,seismo}!rochester!ritcv!jeh
rocksvax!ritcv!jeh
ritcv!jeh@Rochesterkanner@tymix.UUCP (Herb Kanner) (05/07/85)
In article <39@ritcv.UUCP> jeh@ritcv.UUCP (Jim Heliotis) writes: >What is the relationship between f-stops and stops? I think I know what it is >in shutter speeds: > > delta(stops) = log2(old-speed / new-speed) > >sort of like S/N ratios in bels. > >Can anyone tell me the equivalent formula for f-stops? A description of >exactly how they are measured would be nice, too. > The formula is: f = F/D, where f if the f-number, F is the focal length of the lens and D is the "effective lens diameter". If I remember correctly, a more precise definition of D is the diameter of the exit pupil. The exit pupil is the intersection of the cone of rays from an infinitely distant object with the rear principal plane of the lens. I know the last sentence sounds a bit smart-ass, but I can only refer you to a gemometric optics text for further explanation. I don't know how to do it without drawing pictures. The essential point is to think loosely of f as inversely proportional to the lens diameter. Therefore f-squared is inversely proportional to the area, i.e., to the amount of light that gets through. (By lens diameter, of course, I mean diameter taking into account the diaphragm.) Now, for a bit of modelling. Consider a f2 lens of 50mm focal length. It has a certain light-collecting power at its maximum aperture. Now, let us build a camera exactly twice the size, using film that is exactly twice the size of 35mm film, say approx 2' x 3', and put in that camera a f2 100 mm lens. The lens will have twice the diameter, i.e. four times the area of our first lens. But, the light admitted must be spread over four times the film area. Therefore, the ability of the lens to collect light and fling it at the film is seen to depend not on the diameter alone, but on the ratio of the diameter to the focal length. -- Herb Kanner Tymnet, Inc.