If your calculator doesn't handle raising numbers to fractional exponents, you can use the log function to caculate the same thing:
Originally Posted by Kevin Caulfield
You want to find z = 2 ^ (2/3). Tough to do, but easy with the log function:
log( z ) = (2/3) * log( 2 )
log( z ) = 0.20068...
Then, take the inverse log of 0.20068, and you get:
z = 1.58740...
Then, 19 * z gives you 30.16s. You can use this method to determine any fractional stop exposure change. I used the log function which determines logarithms based on '10' - the ln function determines logs based on 'e'. You can use either log function for this task, as long as you're consistent.
Kevin & Ken above give the real mathematical deal - if you have a calculator/computer available, use their equations.
Easier to do sans calculator is to add 25% for +1/3 stop & 60% for +2/3 stop (or subtract 20% for -1/3 stop & subtract 40% for -2/3 stop).
So, 19 secs + 1/3 stop = 19+5(ish)=24 secs. 19 secs - 2/3 stop = 19-8(ish)=11 secs. Not exact, but close enough for most practical purposes.
That is good info. I wonder what the multiplier is for 1/3 stops?
Originally Posted by Bruce (Camclicker)
I am realizing that and additional 2/3 stops worth of time is different than 2 * (1/3 stops worth of additional time).
Maybe I am nitpicking.
Thanks for all the answers!
It's what I posted above. The multiplier for 1/3 stop is 1.26, and for 2/3 stop it is 1.59.
So, Bob's advise above to use 25% for one stop and 60% for two stops is spot on (near enough!!).
Oops, I meant "advice" not "advise".
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A very quick and dirty way to do this and get in the ballpark is to reference the standard ISO progression of films. As an example using 20 seconds (ISO 20) one-third up would be 25 seconds (ISO 25) and + 2/3 stop would get you to 32 seconds (ISO 32). If you had a 12.5 second print (think ISO 125) 1/3 up would be 16 seconds (think ISO 160) 2/3 up would be 20 seconds (think ISO 200).
So, if you memorize the ISO sequence of film speeds, you can relate it to exposure times as well. Since every third number in the sequence doubles, the entire sequence can be derived from just remembering 3 of the ISO speeds. For example, if you can remember ISO 100 (TMX), ISO 125 (Plus-X) and ISO 160 (Portra) you can generate:
...25, 32 , 40 , 50, 64 , 80 , 100, 125 , 160 , 200, 250 , 320 , 400 ...
The jump from 25 to 32 is 1/3 stop just as the jump from 2.5 to 3.2 would be 1/3 stop.