Long term exposure shutter & apateur calculation

[booggerg]

If I want to do exposure upwards of 1 or 2 minutes, isn't there a formula for adjusting the apeature for each incrementally longer shutter speed? Or does that formula fall apart at those extremes?

[edsarkiss]

close the aperture one full f-stop for each doubling of exposure time.

if you were shooting at f/8 for 1 minute, use f/11 for 2 minutes.

the linearity of exposure ratios holds up well, especially on digital cameras where "reciprocity failure" is not present as it was with film.

[pcasciola]

If you are looking for a formula, I guess the simplest would be:
S * (2 ^ F)
shutter speed times (2 to the power of full f-stops down)

For example, going from f/2.8 to f/16 is 5 full stops down, so if you were going to expose for 3 seconds at f/2.8, at f/16 it would be 3 * 2 ^ 5, which is 96 seconds for the same exposure. Simply doubling the exposure time for each full stop is much easier than trying to plug values into a formula though.