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

[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]

Originally Posted by 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 ...

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

[Sparrow]

Originally Posted by rxmd

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]

Originally Posted by DNG

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]

Originally Posted by David Hughes

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]

Originally Posted by sevo

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]

Originally Posted by Sarcophilus Harrisii

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]

Originally Posted by 135format

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]

Originally Posted by sevo

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=KmNIo...layer_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]

Originally Posted by 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.

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.

[sevo]

Originally Posted by 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.

That is one of the neat properties of one single sequence progressing by √2.

[David Hughes]

Hi,

As we are talking about areas of glass you have to square the f numbers and then you'll find they go (roughly) 1 2 4 8 16 etc.

But the figures are cut back to fit on the lens so for F/2.8 we ought to see f/2.8284271 etc. It works for most of us and, given the fudge factor, in the shutter speeds and the actual shutter speeds, light passed by the lens and film exposure latitude, it's minor.

Regards, David

[rxmd]

Originally Posted by David Hughes

But the figures are cut back to fit on the lens so for F/2.8 we ought to see f/2.8284271 etc. It works for most of us and, given the fudge factor, in the shutter speeds and the actual shutter speeds, light passed by the lens and film exposure latitude, it's minor.

Rounding to two significant digits already is more precise than most mechanical shutters and chemical development processes would be.

[Pherdinand]

Originally Posted by sevo

That is one of the neat properties of one single sequence progressing by √2.

it's not so surprising, really. It is self-determied by the fact that surface has units of length times length (=basic math) and the photographic requirement that we want to know "how big must the aperture be in order to double the received light" which is completely up to us to define.
If we were talking about volume, instead of surface, e.g., calculating how wide (or tall, or long) you have to make a cube-shaped box to fit a certain nr of toilet paper rolls then the series would be cubic root of 2 and would, again, double.
Or if, for whatever reason, we would be interested in tripleing the light that passes through the lens, then we'd have to use √3, and therefore there would be 2 series of tripleing intermixed

Indeed the "next stop" in this learning process is T-stops
but that loses relevance since the invention of proper anti-reflection coatings, coz the transmission of the lens elements is almost 100% therefore T-stops are only a tiiiny bit smaller than F-stops.

[DNG]

Quote: Originally Posted by DNG

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. END QUOTE

wolves3012 said
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.

Yes, this is true also, although, I leave the ubber tech to the mathematician! in all practical none tech photographic applications, the small variance in light transmission, is a non issue. The way we arrive at number f/1.4, f/2.8 etc.. is beyond my math skills. BUT, That may be the OP question also.

[Dwig]

Originally Posted by DNG

in all practical none tech photographic applications, the small variance in light transmission, is a non issue.

Actually, the variance is often fairly large (~1/2stop or greater) in very complex optical designs. For almost all still photography users, it is completely compensated for by the ubiquitous TTL metering found in cameras that accept such complex optical designs (read: zooms). It is only a real exposure concern to cine shooters, and cine lenses are frequently calibrated in T-stops rather than f-stops.