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04-23-2008, 10:04 AM   #1
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How many stops difference formula

was looking at FA Limiteds and was wondering how many stops difference they were from other standards apertures. So looked around and based upon the formula on Wikipedia for Aperture Area, the formula is as follows:

Difference in Stops = Slower Aperture^2 / Faster Aperture^2 - 1

my DA21 e.g. is f3.2, so 3.2^2 / 2.8^2 - 1 = 0.31, so about 0.3 stops slower than f2.8
thought this might be handy...

04-23-2008, 10:20 AM   #2
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I'm sure there's an empirical way to do this - mount your fastest lens, and set your exposure steps to 1/3 stop... then note what apertures pop up as you change the aperture by wheel - and you'll even see what the corresponding shutter speed effects are. I think this would work, can't check because I'm at work and my camera isn't.
04-23-2008, 05:42 PM   #3
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that might work using a manual exposure and then setting the AE Lock
04-23-2008, 08:47 PM   #4
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QuoteOriginally posted by k100d Quote
that might work using a manual exposure and then setting the AE Lock
I have run into this situation before and Nesster has it right.

<<my DA21 e.g. is f3.2, so 3.2^2 / 2.8^2 - 1 = 0.31, so about 0.3 stops slower than f2.8
thought this might be handy...>> And that is handy. This took me a very long time to figure out, probably because my teenagers are sucking the life out of me and my brain.

Wendy

04-23-2008, 09:06 PM   #5
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QuoteOriginally posted by k100d Quote
was looking at FA Limiteds and was wondering how many stops difference they were from other standards apertures. So looked around and based upon the formula on Wikipedia for Aperture Area, the formula is as follows:

Difference in Stops = Slower Aperture^2 / Faster Aperture^2 - 1

my DA21 e.g. is f3.2, so 3.2^2 / 2.8^2 - 1 = 0.31, so about 0.3 stops slower than f2.8
thought this might be handy...
So.... another way to do this is to find out the ordinal (counting) value of the stop. By that I mean, count with f/1 as the 0th stop, f/1.4 as the first, f/2 as the second, etc. This can be done with this formula:
log(stop number)/log(sqrt(2))
Which gives, rounded to two digits, this:

Code:
f/1.4 = 0.97
f/2 = 2
f/2.8 = 2.97
f/4 = 4
f/5.6 = 4.97
f/8 = 6
f/11 = 6.92
f/16 = 8
Which is probably overly precise, because manufacturer's tolerances and just plain fudging are probably a lot bigger than this rounding error. So, f/2.8 is about the third stop. The formula log(3.2)/log(sqrt(2)) gives ~3.36, or, again, about a third of a stop slower.

Maybe this is too geeky, but I find it a more intuitive way to look at it than the simpler but more magical ^2/^2-1 approach. Your mileage may vary.
05-16-2008, 06:04 AM   #6
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mattdm is right.

The original formula is wrong, it doesn't give the difference in f-stops. It gives the relative difference in light.

The correct formula would be:
Code:
Difference in Stops = log (Slower Aperture^2 / Faster Aperture^2) / log (2)
or, which is exactly the same (and you may use whatever log you like ):
Code:
Difference in Stops = (log (Slower Aperture) - log(Faster Aperture)) / log (sqrt(2))
(mattdm's formula)

It gives you 0.39 (rather than 0.31). That's only close by accident, in other cases the difference will be huge...
05-16-2008, 06:20 AM   #7
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arrgghhh . . .too much math - my head hurts

but thanks anyway guys
05-16-2008, 06:29 AM   #8
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I can't see how this could be of any use to me, but it's still nice to know.

05-16-2008, 06:35 AM   #9
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QuoteOriginally posted by mattdm Quote
f/2.8 = 2.97 [...] Maybe this is too geeky
Einstein says: make it as simple as possible, but no simpler

BTW, f/2.8 = 3 is correct by definition, 3 is the exact value, 2.8 is the one which was rounded.
05-16-2008, 07:01 AM   #10
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QuoteOriginally posted by falconeye Quote
Einstein says: make it as simple as possible, but no simpler

BTW, f/2.8 = 3 is correct by definition, 3 is the exact value, 2.8 is the one which was rounded.
correct F2.8 is actually F2.828

ALso note when people talk about 1/3 stop faster lenses, the origonal K mount definition for the coding of apatures only works in 1/2 stops, not thirds.

the maximum apature coding is the following range of apatures
1.4, 1.7, 2, 2.5, 2.8, 3.5, 4, 4.56, 5.6, 6.7, 8

Any other maximum apature might be available in Av mode but not manual, unless they do something funny with the data transmitted on the 7th pin which gives all the lens data focus distance focal length etc.
05-16-2008, 07:54 AM   #11
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Falconeye gave the correct formula. And it really cannot get any simpler than that.

Having a calculator handy helps, of course
05-16-2008, 08:30 AM   #12
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I use the following handy chart I made some time ago, which will only look good viewed in a fixed-pitch font:

full stops: 1.0 --- --- 1.4 --- --- 2.0 --- --- 2.8 --- --- 4.0 --- --- 5.6 --- --- 8.0
1/3 stops: --- 1.1 1.2 --- 1.6 1.8 --- 2.2 2.5 --- 3.2 3.5 --- 4.5 5.0 --- 6.3 7.1 ---

Simply count along the number line.
05-16-2008, 08:47 PM   #13
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QuoteQuote:
(slower/faster)^2 - 1
i was thinking about this more the other day and realized that my formula didn't represent the difference in stops, but only the relative difference in area of light received into the lens.

because the number of stops increases by 1, everytime the area doubles
therefore, the stops difference
= ln (slower/faster)^2 / ln(2)
= 2 ln(slower/faster) / ln (2)
= ln(slower/faster) / 0.5ln(2)
= ln(slower/faster) / ln(sqrt(2)) <- which is basically mattdm's formula

sorry, should have picked up on my mistake earlier...
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