# A moderately Technical Discussion about f stops.

Discussion in 'Casual Photo Conversations' started by Henricvs, Jan 22, 2019.

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1. ### chuck909

The Pizza Pi rule is easier - an 11" pie is twice as much pizza as an 8" pie, a 16" pie is twice as much as an 11" pie.

2. ### alan_marcus|2

A tip of the hat to chuck909 -- therebefore this Pizza rule was unknown to me! You get an A+

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3. ### Bill C

Personally I think the easiest way to "remember" the whole f-stop number sequence is coming to the realization that the f-numbers double for every second stop. It's not so easy to muliply a number by 1.4 in your head, but... It's pretty easy to double (or halve) the f-numbers.

So if you can just remember two f-numbers next to each other... say f/1.0 and f/1.4, follow the sequence like so: double the 1.0 to get f/2.0, and double the 1.4 to get f/2.8. Then double the 2.0 to get f/4.0, and double the 2.8 to get f/5.6, etc.

If this is not real obvious, look at it this way: start with the numbers f/1.0 and f/1.4. From f/1.0, write down the sequence of doubling numbers: 1, 2, 4, 8, 16, 32, etc. Then, in between these numbers, write down the other doubling sequence: 1.4, 2.8, 5.6, 11.2 (round it to f/11), 22, etc.

This will give you the f-number sequences as far as you want to go, aside from those little idiosyncrasies in rounding off.

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4. ### rodeo_joe|1

I'm sure all of this makes it crystal clear to a beginner exactly what the effect on the picture is if they change the aperture number from 2 to 8.

Getting bogged down in theory and technical nitty-gritty is the enemy of making good pictures. Nobody needs to know the area of the aperture 'hole' to apply f-numbers practically. The numbers are what they are, and could just as easily be marked 1, 2, 4, 8, 16 etc. like they are on some old enlarging lenses.

The point is to make the association of a particular number with its visual effect, and secondarily how it affects the exposure. And nobody needs to know how the numbers were arrived at to do that.

They just need to know that f/4 lets in twice as much light as f/5.6, and that f/2.8 lets in twice as much light again. A simple relationship like - 'If you make the aperture number bigger by a step, you need to make the shutter speed smaller by a step' is about all that's needed. Apart from by the terminally curious.

We're not living in the stone age. We can (mostly) leave the tedious calculations to the camera now, and concentrate on the important bit of what's in front of the camera and seen through the viewfinder.

Last edited: Jan 24, 2019
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5. ### Ludmilla

Fascinating stuff.

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6. ### Henricvs

Thanks to everyone who contributed to correct my screwup. Especially, Big Al Marcus. I would have loved your class!

Best,
Henry

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7. ### alan_marcus|2

@ Rodeo_Joe --
Does knowing the technical stuff make you a better photographer? Maybe not but it doesn’t hurt. Knowing the technical stuff brought fame and riches to Ansel Adams. Possibility a kid with a camera phone will win the Pulitzer Prize by just being there and taking a praiseworthy picture. In-between is the casual photographer and the professional photographer. Some pros just naturally get it. Some pros get it by osmosis. Some pros study for years to get it. As for me, never famous but 55+ years of being well employed and enjoying every minute.

8. ### Henricvs

I enjoy learning new things and understanding how and why on just about all my interests, including photography. I'm a slow learner, but I never give up.

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9. ### James G. DainisModerator

Area varies as the square of the linear measure. Even engineers sometimes forget that.

"This 4 inch diameter water line is plugged. I will use two 2 inch lines to bypass it." Sorry that will provide for only 1/2 the flow. You would need four 2 inch lines to bypass and get the same area and flow as the 4 inch line.

4^2 = 16

2^2 = 4

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10. ### paul_noble

Do the math (its easy).

Pick a focal length. It really doesn't matter. Let's say 50mm.

Calculate the area of the circle formed by the iris at f/1.4. A = ((50/1.412)/2)**2 * pi (the answer is 984 mm**2)

Now calculate the area of the iris at f/2 A = ((50/2)/2)**2 * pi (the answer is 490 mm**2), or half the area of the circle at f/1.4.

So, an aperture of f/2 admits exactly half the light per unit of time that an aperture of f/1.4 does. Conversely, f/1.4 admits twice the light that f/2 does.

It is left as an exercise for the interested student to perform similar calculations for f/2.8, f/4, f/5.6, f/8 and so on. You will find that, at each step, the area is half (allowing for rounding) the area of the previous step.

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11. ### rodeo_joe|1

- And that's why he thought that Zone VIII - described as white with detail, which could realistically have no more than 100% Lambertian reflectance - was 3 stops more than Zone V, which is firmly stated as having 18% reflectance?

By my calculation 3 stops (8x) more than 18% = an improbably high 144% reflectance.

So much for Ansel's technical prowess.

What brought him fame and riches was his eye for a good landscape composition, being an excellent printer, and all the books he wrote off the back of it.

I'm sure that trying to follow the Zone system has led to far more wrong exposures than right ones, and only B&W film latitude has saved the wrong 'uns.

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12. ### alan_marcus|2

@rodeo_joe|1 -----

Actually an 18% gray card expressed as a decimal fraction = 0.18.
This is because percent means per 100.
Thus the math
Double 18% = 0.18 X 2 = 0.36 = 36% (a 2X change = 2 f-stops delta (4X)
Double again 0.36 X 2 = 0.72 = 72% (another 2x change = 3 f-stops delta (8X)

Perhaps Ansel Adams and is partner Fred Archer nailed the zone system they conceived in 1930. The 18% gray target became the de facto calibration point for most all light measuring instruments. A tip of the hat to the men who provided a bridge between the science of sensitometry (film measurement) and exposure determination.

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13. ### BeBu Lamar

He actually gave Zone VII 3 stops more exposure than Zone V but the resulting negative density is only about 1.8 stops denser or in other word 0.54 density more. So it's still well within the film dynamic range.

14. ### alan_marcus|2

@BeBu Lamar -- You are spot on. The slope or gamma of pictorial film is 0.8. In other words, if it were 1, the slope angle would be 45 degrees and you would get full value for each f-stop change. A gamma of 1 has proven to be too contrastry so pictorial films have on average a slope angle reduced to about 36 degrees which works out to be 0.8. Thus for each 1 f-stop change you only get 0.24 density units not the 0.30 density units if the film had a gamma of 1.0

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15. ### glen_h

There is an article in wikipedia that says that negative fiims have gamma less than one, and reversal films more than one.

For negative films, besides the reasons you say, less than one give more exposure latitude that you can undo
with appropriate gamma in printing. Lower gamma makes film exposure easier, but printing harder.

But for slides, there is no printing step, so it has to have the appropriate gamma in the first place.

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16. ### rodeo_joe|1

@ Bebu & Alan.
Read Ansel Adams' books!
It's quite clear from the technical sections that each zone is equated to exactly one stop difference in exposure. This is quite obviously shown on the H&D graphs that he had John Sexton produce.

It doesn't matter how you express the reflectance of a surface; as a decimal or as a percentage. Multiplying 18% or 0.18 by 8 still gives you 144% or 1.44, either of which is way above the reflectance of fresh snow, a whitewashed wall, a fluffy white cloud, or any other matt white surface you care to name. In short Zone VIII is overestimated by one half stop.

The density produced on film is irrelevant to the metering and exposure process, and as is also clear to anyone familiar with the zone system, is regulated by the development time. That's the whole point of the zone system. Or it would be if based on accurate data.

However, if the zones as described aren't actually one stop apart - and they're not - then it puts a big question mark over the whole over-complicated procedure.

The error is easily tested by using a digital camera these days. Applying +2.5 stops compensation to an exposure reading taken from an 18% grey card takes it to white, and just short of overexposure. While 3 stops compensation induces overexposure 'blinkies'.
Conversely, metering from a matt white surface and applying -2.5 stops compensation renders the surface as 18% grey.

My theory is that Adams' background as a concert-standard pianist puts everything in perspective: That the zone system has a parallel in music notation, and is just as arcane and illogical to other than its initiates.

If you think of Zone V as 'middle C' then Zone VIII is equal to note F, which is only 2 tones and a semitone up. Not 3 whole tones.

I suspect Adams' was confusing musical notes with zones, and just failed to mentally scribble in the sharps and flats.

"There is an article in wikipedia that says that negative fiims have gamma less than one, and reversal films more than one."

Wikipedia is correct, but that has absolutely nothing to do with exposure determination. Non-sequiter arguments that distract from Adams' blatant error just don't wash I'm afraid!

Last edited: Jan 28, 2019
17. ### The Shadow

I certainly don’t think it has to hurt, but I do think it can hurt. For some, these technical discussions can supplement and support an artistic vision. For some, concentration on technique can very well overwhelm or substitute for it. I think Adams was a master technician and printer and gave a lot to photography and photographers. I think he was less an artist. Whether his love for printing and photographic techniques took away from more creative visual potential, I do not know, but I don’t think the two went hand in hand for him.

18. ### alan_marcus|2

@ The Shadow --

Ansel Adams and his cohorts lived and worked in an era void of camera automation. The hand-held electric light meter had just emerged. They chose to use giant cameras because film and enlargement techniques were not up to snuff. The point is, getting the exposure “right” was paramount. They needed to acquire the technical stuff -- otherwise they used trial-and-error. 21st century photographers can concentrate on composition, ignoring the technical, it’s OK if you let the camera do the thinking.

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19. ### James G. DainisModerator

I take a gray card reading and it reads 1/500 - f/16 which is Zone V.
I take a shot at 1/250 - f/16 and that is one stop more or Zone VI.
I take another shot at 1/125 - f/16 and that is another stop more or Zone VII.
I take another shot at 1/60 - f/16 and that is another stop more or Zone VIII.

Going from Zone V to Zone VIII is a three stop difference. Ansel is quite clear about this in his book, The Negative.-

..."we define the one-stop exposure change as a change of one zone on the exposure scale, and the resulting gray in the print is considered one value higher or lower on the print scale."

As far as I can tell, 99% of his references to exposure/Zones is given as direct exposure stops not sensitivity readings.

20. ### BeBu Lamar

I will give you full explanation after I reread the books. But I know Adams didn't care for subject reflectance only his prints.