View Full Version : Lens Trivia: Figuring Half-Stops
Mark Sawyer
9-Mar-2016, 14:26
Just a little lens trivia some may not know...
Most all of us have the standard f/stops memorized: 1, 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, 32, 45, 64, 90...
And most of us know that the value doubles every other stop...
But do you know how to figure what the half-stop is in-between the standard stops?
Say you have an f/6.3 Tessar, an f/6.5 Cooke Series III, an f/6.7 Fujinon W, and an f/6.8 Dagor. Which is exactly mid-point between f/5.6 and f/8?
Anybody know how to figure it? It's pretty simple!
Kevin Crisp
9-Mar-2016, 14:55
When the pointer is right between two numbers?
Mark Sawyer
9-Mar-2016, 15:02
When the pointer is right between two numbers?
Nope! We're talking an actual numerical value!
I was going to give the same flippant answer, but it's logarithmic and thought I heard of an easy remembrance to help out. f/5.6...f6.3.^.f7.1...f/8.
David
https://en.wikipedia.org/wiki/F-number
It all explained there.
photog_ed
9-Mar-2016, 15:41
A quick way to figure it is to multiply the next lower F/# by 2^(1/4) = 1.189.
Ed
Mark Sawyer
9-Mar-2016, 16:34
I was going to give the same flippant answer, but it's logarithmic and thought I heard of an easy remembrance to help out. f/5.6...f6.3.^.f7.1...f/8.
David
Nope, those are third-stops, and I don't want to memorize the whole scale...
https://en.wikipedia.org/wiki/F-number
It all explained there.
They don't explain how to figure half stops, (and some of what they do explain is wrong...)
A quick way to figure it is to multiply the next lower F/# by 2^(1/4) = 1.189.
Ed
There's a quicker way...
To find a half-stop, just add the two stops that are lower than the stops on either side. So for the stop half-way between f/5.6 and f/8, just add 2.8 and 4. So f/6.8 is half-way between! Half-way between f/16 and f/22 would be 8 +11 = f/19. Etc...
You missed the "^".:) So, now tell why I should care if it is 6.8 or 6.6596.
David
Jac@stafford.net
9-Mar-2016, 17:12
We can calculate fractional F-stops to the end of math, but neither our lenses nor shutter speeds are accurate enough to matter.
.
Mark Sawyer
9-Mar-2016, 17:14
...So, now tell why I should care if it is 6.8 or 6.6596.
David
We can calculate fractional F-stops to the end of math, but neither our lenses nor shutter speeds are accurate enough to matter.
.
That's why it's lens TRIVIA!
Kevin Crisp
9-Mar-2016, 17:26
Practical answer does not equal flippant answer.
Paul Metcalf
9-Mar-2016, 17:27
Thanks Mark. I appreciated this.
photog_ed
9-Mar-2016, 19:46
Nope, those are third-stops, and I don't want to memorize the whole scale...
They don't explain how to figure half stops, (and some of what they do explain is wrong...)
There's a quicker way...
To find a half-stop, just add the two stops that are lower than the stops on either side. So for the stop half-way between f/5.6 and f/8, just add 2.8 and 4. So f/6.8 is half-way between! Half-way between f/16 and f/22 would be 8 +11 = f/19. Etc...
OK, this bothered me all day, so I worked it out. This is an approximate method that depends on the approximation 2*sqrt(2) ~ 3. So if 2.828... is close enough to 3 for you then you are good to go.
Ed
Struan Gray
10-Mar-2016, 04:02
Actually, you are solving the quartic equation
x^4 + x^2 - x = 0
There are four roots. two of them are complex. None of them are the forth root of two.
I prefer to just write out the sequence
Best wishes --- Allen
1/2 stops calculate by factor 2^(1/4)
1/3 stops calculate by factor 2^(1/6)
1/2 stops: f/1 f/1.2 f/1.4 f/1.7 f/2 f/2.4 f/2.8 f/3.4 f/4
1/3 stops: f/1 f/1.12 f/1.26 f/1.4 f/1.6 f/1.8 f/2 f/2.2 f/2.5 f/2.8 f/3.2 f/3.6 f/4
1/2 stops: f/4 f/4.7 f/5.6 f/6.7 f/8 f/9.5 f/11 f/13 f/16
1/3 stops: f/4 f/4.5 f/5 f/5.6 f/6.3 f/7 f/8 f/9 f/10 f/11 f/13 f/14 f/16
1/2 stops: f/16 f/19 f/22.6! f/27 f/32 f/38 f/45 f/54 f/64
1/3 stops: f/16 f/18 f/20 f/22.6! f/25 f/28 f/32 f/36 f/40 f/45 f/51 f/57 f/64
1/2 stops: f/64 f/76 f/90 f/108 f/128
1/3 stops: f/64 f/72 f/81 f/90 f/102 f/114 f/128
Jac@stafford.net
10-Mar-2016, 15:15
This has been an academically interesting discussion, but our LF lenses are so likely to have inaccurate shutter speeds that FAPP I would ignore 1/2 F-stop nuances.
.
Doremus Scudder
11-Mar-2016, 02:50
This has been an academically interesting discussion, but our LF lenses are so likely to have inaccurate shutter speeds that FAPP I would ignore 1/2 F-stop nuances.
.
I doesn't hurt to try and be a little more accurate. I have a shutter-speed tester that I use to find the actual speeds on all my shutters and then label the lensboard with speeds to the closest 1/3 stop. I then use intermediate aperture settings, also in 1/3-stop increments to get my exposures as close as I can (while being aware that there is an inherent margin of error in the system).
FWIW, a whole stop underexposure with transparency materials will yield an unusable slide... even a half-stop is pushing it. Striving for accuracy in exposure is the only way to get even close. Ignoring a half-stop "nuance" that is compounded by other errors in the system can result in severe exposure problems.
One-third-stop increments are how my meter reads, how film speeds are indicated and how filter factors and graphs of curves, etc. are marked. I see no reason to use half-stop increments instead, although it's interesting to know.
Best,
Doremus
Same here, except I've not tested my shutter speeds. My meter is set in thirds and most of my lenses are marked in thirds. I just do not sit down and calculate or try to remember the approximation for the actual f/stop number. I'm happy with keeping that in the black box.
David
hell.. as sloppy as I am with my development times... a third stop here or there taint pis
Jeff Keller
11-Mar-2016, 19:30
Square root of the square root of 2 = square root of 1.4142 = 1.1892
either divide or multiply to go down or up. It is proportional to the area of the lens which increases with the square of the radius.
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