In article <32ae24cb.6295997@news.knox.mindspring.com>, mtnavy@mindspring.com says...

>Is there a known relationship between pairs of film speed and f-stop
>combinations? By that I mean, for example, does a film speed of 400
>used with a f5.6 lens correspond to using a film speed of 200 with a
>f2.8 lens (for the same shutter speed)?

Relating film speed (light sensitivity rating), shutter speed, and f-stop
(diaphragm opening in the lens) are how we control exposure - without a relationship, exposure control would be impossible. The shutter is obvious: each halving or doubling of the shutter time exposes the film half or
twice as much as the previously selected shutter speed (1/125th is 1/2
as long as 1/60th, etc.). The film speed is less obvious, but simple:
doubling or halving the ASA number corresponds to a one stop change in
exposure (400 ASA is twice as "fast" as 200 ASA, etc.) - the inbetween
numbers allow for 1/3 stop speed ratings (400, 320, 250, 200, 160, 125,
100, etc.). The f-stop is also easy to understand if you realize that the number is not arbitrary, but is the fraction of the focal length of the
lens (infinity focus) divided by the diameter of the hole that the light
goes through (determined by the lens diaphragm, set in stops [or fractions
of stops]). (For a simple lens, this is true - there are complications,
but for this purpose, it works.) So a 50mm lens set at f4 would have a diaphragm hole size of 50mm/4 = about 12mm. If I reset the f-stop to f8,
the hole size would be 50mm/8 = about 6mm. Since the AREA of the diaphragm
hole is what counts for accounting for the amount of light going through
the lens (not just the diameter, but the squared radius for finding area), doubling or halving the f-stop number results in a 2-stop exposure change, which explains the use of the inbetween numbers for halved or doubled
exposure (1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, 32 are the whole-stop
numbers). So, in your example, a 400 ASA film used with the lens at f5.6
would give the same density on the processed film as 200 ASA film used
with f4 (with shutter speed and subject lighting kept the same).
Hope This Helps