why are f-stops 2, 2.8, 4, 5.6, 8, 11?

[Sarcophilus Harrisii]

Take a look at the leftmost column (this is from the Wikipedia article http://en.wikipedia.org/wiki/F-number quoted above). Your lens is in what the table calls the US system and goes from 4 (f/8 in modern terms) to 128 (f/45).

Brilliant, thanks! I've learnt something new today.
Regards
Brett

 

[rxmd]

it's arbitrary because why pick 1? So why is my 35mm Elmar labeled 3.5/4.5/6.3/9/12.5/18. Why at some point did Leica Change to 1/1.4/2,etc?

Was there a standard, code or other international ruling body? I don't think so, or at least I never seen one.

Just asking. It probably started to become standardized when the ASA (American Standards Association) promulgated standards for determining film speeds.

If someone can point out a Country specific or International Standard (such as ISO) then I will agree it is not arbitrary.

Basically all you're quibbling about is what constitutes an "arbitrary" agreement.

You are saying any agreement is arbitrary until a standards body is involved. In your logic, standards bodies alone have the power of conferring non-arbitrariness. According to you, everything is arbitrary until someone puts a stamp on it, and the word "arbitrary" is synonym of "not really official", "not officially endorsed by the right people".

Roger and others are arguing that the f/stop system expresses a ratio between two lengths, and that 1 is a mathematically special and beautiful ratio. Consequently, denoting your stops so that they start with 1-1.4-2 is less arbitrary than alternatives such as 1.1-1.6-2.2 on the same series.

I would tend to agree with the latter, because standards bodies, while useful, are basically glorified labeling institutions, while the elegance of the latter system comes from the underlying mathematics of the system itself.

The reason Leica put the 3.5-4.5-... scale on early Elmars is, as Sevo has pointed out, that Leica just took the open aperture 3.5 and then full stops from there. The disadvantage of this system is that you end up with different f-stop series on all your lenses, depending on their starting apertures. That's why Leica eventually switched to the system everybody else was using.

 

[Roger Hicks]

it's arbitrary because why pick 1? So why is my 35mm Elmar labeled 3.5/4.5/6.3/9/12.5/18. Why at some point did Leica Change to 1/1.4/2,etc?

Was there a standard, code or other international ruling body? I don't think so, or at least I never seen one.

Just asking. It probably started to become standardized when the ASA (American Standards Association) promulgated standards for determining film speeds.

If someone can point out a Country specific or International Standard (such as ISO) then I will agree it is not arbitrary.

There is allegedly a British Standard of 1949. Although I have no further reference for it, the Focal Encyclopedia refers to this series being adopted from an existing international standard.

Apart from that, as RXMD points out, "1 is a mathematically special and beautiful ratio".

Cheers,

R.

 

[sevo]

The reason Leica put the 3.5-4.5-... scale on early Elmars is, as Sevo has pointed out, that Leica just took the open aperture 3.5 and then full stops from there.

Not entirely - early on there have been lenses that used sequences offset by a half stop (starting at f/6.7) or 2/3 stop (f/7.1). And cine and process lenses using t stops often were engraved with full stops off the start even recently.

But the dominant scales after WWI were our modern base 1 scale and the so-called "old" scale, which is 1/3 stop offset to the former, starting at f/3.2. Which not quite incidentally is √10, so that the full "old" scale ended at a pleasingly symmetric hundred (3,2–4,5–6,3–9–12,5–18–25–36–50–71–100).

 

[Sparrow]

... I think they should make the √2 = 1.5 that would make everything much more simple ... and they could make pi = 3 at the same time ...

 

[rxmd]

... I think they should make the √2 = 1.5 that would make everything much more simple ... and they could make pi = 3 at the same time ...

Great idea... in the spirit of the famous 1897 law from Indiana declaring pi =3.2.

 

[Sparrow]

Great idea... in the spirit of the famous 1897 law from Indiana declaring pi =3.2.

... really! marvellous 🙂

 

[David Hughes]

Interesting thread but no mention of the 1900 Paris convention to sort it out that settled on f/1 etc.

BTW, in the chart shown previously "US" means Universal Scale and not what some may think. Nor is it a reference to the United States of Holland...

Regards, David

 

[wolves3012]

it does not matter what Focal Lentgh lens you are using.
If you have a good exposure with your 50mm lens at f/4, you can put your 100mm lens on and use f/4,
and you will get the same exposure value (for the knit pickers, move back with the 100mm lens to cover the same framing)

f/4, or any f/stop, is one consistent you can count on when using different lenses for the same lighting.

This is reasonable in most cases but it's not quite true. Two lenses at the same f-stop are not guaranteed to give the same exposure, since it also depends on the lens' light transmission. T-stops are equal-illumination points (and therefore equal exposure for a given shutter speed), not f-stops. Of course, most lenses aren't marked in t-stops, so f-stops is the best you can do with them.

 

[sevo]

Interesting thread but no mention of the 1900 Paris convention to sort it out that settled on f/1 etc.

Did it? The vague literature I have read described it in a way that I always believed it to have been the origin of the Universal Scale. But then there seem to have been two Paris conferences (1889 and 1900) - maybe that was the other one.

 

[David Hughes]

Did it? The vague literature I have read described it in a way that I always believed it to have been the origin of the Universal Scale. But then there seem to have been two Paris conferences (1889 and 1900) - maybe that was the other one.

Hi,

I've been looking for my source on and off all day but haven't found it yet. Mainly because my sources are paper ones, like books.

BTW, for "Universal System" read "Uniform System".

Regards, David

 

[Muggins]

Brilliant, thanks! I've learnt something new today.
Regards
Brett

Likewise - it's not often that you get a question answered that thoroughly in one post!

Thank you, RXMD.

Adrian

 

[135format]

What about waterhouse stops?

 

[rxmd]

What about waterhouse stops?

Well, what is your question?

Waterhouse stops are discs inserted into a slot in the lens. The discs have differently-sized holes that serve as apertures. You change the aperture literally, by changing the disc.

There isn't really a uniform way of marking Waterhouse stops. Finding out the f-number of a given stop therefore can be tricky. Some later ones have markings with the f-number, then it's easy. Others are marked with the diameter, or with a running series (#1, #2, ...). In the worst case you have to measure them and use the f-number formula to calculate the f-number.

The f-number formula is f/d, where f is the focal length of the lens, and d the diameter of the entrance pupil. The entrance pupil is not simply the front lens, it's the front lens as viewed through the aperture (otherwise the f-number wouldn't change when you change the aperture). I'm not sure if there is an obvious way to measure the entrance pupil directly. I guess you could put a transparent plastic ruler as close to the front lens as possible and look at it through the back of the lens through the aperture and see how much of the ruler is visible.

 

[Roger Hicks]

Did it? The vague literature I have read described it in a way that I always believed it to have been the origin of the Universal Scale. But then there seem to have been two Paris conferences (1889 and 1900) - maybe that was the other one.

According to the 3rd edition of the Focal Encyclopedia (usually reliable), the RPS proposed the Uniform System in 1881.

By the way, thanks for the comparative table from 1899. There seem, indeed, to have been more systems than I realized, but they seem to have been on the way out in 1900.

Intriguingly, my Ilford Manual of Photography, (120th thousand, c. 1901?) seems to make no mention of apertures, though I have not tried to read it in detail for years.

Cheers,

R.

 

[peekpt]

Better explanation so far (video) http://www.youtube.com/watch?v=KmNIouLByJQ&feature=player_embedded

 

[David Hughes]

Hi,

Seeing this again immediately reminder me that the source for it (my previous but one post) was Kodak's book "How to make Good Photographs" and any edition from the 19th century onwards will tell the story but it's best to read them in the correct sequence.

I've no copies later than the mid 30's and that covers it fairly well. They come up from time to time on ebay at all sorts of prices or else try the booksellers collation.

Regards, David

 

[someonenameddavid]

the ratio based on the square root of two works very well with shutter speeds that are sequenced 1/30 1/60 1/125 etc, not so much with earlier shutters. Where my thoughts get befuddled are on the DIN speed numbering of film, semi-logarithmic where sensitivity doubles for every three units of DIN.

David

 

[sevo]

the ratio based on the square root of two works very well with shutter speeds that are sequenced 1/30 1/60 1/125 etc, not so much with earlier shutters.

The earlier sequence has mostly been essentially the same, only the nominal speeds printed on the shutter differed. FWIW the modern series does not display the accurate powers of two either, but shows e.g. a friendly 500 instead of the true 512. In either case, no shutter I am aware of ever made the special provisions to match the irregularity of the series, at least for speeds shorter than 1/10s - once outside the slow speed escapement range, the timer geometry usually progresses in steady 1/2 steps.

 

[ramosa]

i don't think this has been mentioned. but what i find interesting is that f-stops seem to double in a way. look at 1, 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22. there are two sequences of near doubling. the first from 1 to 2 to 4 to 8 to 16. the second from 1.4 to 2.8 to 5.6 to 11 to 22.