F1.8 vs F3.2

[mpenza]

Say I take a 1s shot using F1.8. How many seconds would it take for a F3.2 lens to get the same level of exposure? Are there any formula I could use?

[Jed]

I'm sure there's a complex mathematical formula somewhere, but use the following table until someone coughs it up:

f1.4
-- f1.6
-- f1.8
f2.0
f2.8
-- f3.2
-- f3.5
f4

Each figure on the left column is a full f-stop, while the indicated figures on the right at the universally accepted (for convenience) 1/3 stops.
So f1.8 is 1 and 2/3 stop faster than f3.2, hence you should use that amount a lengthier shutter speed, or 3s.

[YSLee]

f/3.6 will be 2 stops faster than f/1.8, so f/3.2 will be slightly less than 2s?

[Jed]

No, two stops away from 1s is 4s (1s, 2s, 4s, 8s, etc.) So it's slightly less than 4s.

[mpenza]

Thanks guys for enlightening me!

So, roughly every "1.414" times is one stop loss in light requiring doubling of the exposure time right?

[Jed]

Yes that's right. Cause apertures are measured as a reciprocal ratio of the diameter, area wise. Hence the number is achieved by a root of two, which is 1.414 etc as you point out.