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

[Hjortsberg]

why not 3, 6.5, 9, 12? sorry if this is a really dumb question. just stated this hobby about a year ago.

 

[rxmd]

There is a "German" f-stop series that goes 1.6 - 2.2 - 3.2 - 4.5 - 6.3 - 9 - 12.5 - 18 - 25 - 36. You can find that on older Leica lenses for example. I think the main reason why German manufacturers stuck to this different series for a while was because it allowed them to sell their own lightmeters and accessories.

The "classic" series 1 - 1.4 - 2 - 2.8 and so on is of course completely equivalent, except that it makes it more obvious that you are operating with square roots of 2. Also 1 and 2 in the series are numerically more obvious choices as the starting point for a series (after all the f-stop number is the relation of focal length to entrance pupil of the lens) than 1.6, 3.2 or 9.

 

[Hjortsberg]

obviously i never paid much attention in math class.

Hell, this is a hobby for me. It's actually kinda amusing how bad I am at it. Gives me a good laugh!

 

[erpe]

There is a wiki article about this http://en.wikipedia.org/wiki/F-number
It's a common question and not too obivous for starters.

 

[n5jrn]

Because the f-numbers they refer to are the focal length of the lens divided by the effective diameter of the aperture, but how much light a circular aperture passes is a function of its area, not its diameter. Given that the area of a circle is proportional to the square of its diameter, that means that any number related to the diameter must change by a factor of the square root of two (approximately 1.4) in order for successive stops to double or halve the amount of light.

Why express apertures in relation to focal length like this? Because a wide lens maps light from a wider field of view onto the same area of film (or digital sensor), an aperture of a given absolute diameter will project more photons onto that film or sensor area if it's for a wide-angle lens as opposed to a telephoto. With f-numbers, if an exposure of 1/125th at f/8 is correct for a wide lens, those settings are also correct on a normal or telephoto lens.

 

[sevo]

There is a "German" f-stop series that goes 1.6 - 2.2 - 3.2 - 4.5 - 6.3 - 9 - 12.5 - 18 - 25 - 36. You can find that on older Leica lenses for example. I think the main reason why German manufacturers stuck to this different series for a while was because it allowed them to sell their own lightmeters and accessories.

It is the same scale, just a different starting value. But that method of scaling in a full stop progression from the exact (usually by a third or half stop) start value already became unpopular before light meters became widespread - from the mid thirties on it was more common to have only the first stop out of line for lenses whose start opening did not fall on the main scale (the one starting at 1).

 

[Beemermark]

why not 3, 6.5, 9, 12? sorry if this is a really dumb question. just stated this hobby about a year ago.

Because as some point in time, a major (and popular) manufacturer arbitrarily selected 2, 2.8, etc.

if you start looking at 19th century and early 20th century lens (esp large format) you'll see all kinds of F stops.

And it's not a dumb question, rather good one I think,

 

[BobYIL]

why not 3, 6.5, 9, 12? sorry if this is a really dumb question. just stated this hobby about a year ago.

They are not random numbers at all.. They actually start with 1, then 1.4 and 2, 2.8, 4, 5.6, 8... etc. are the multiples of the square root of two (1.41421..); meaning with each step to the left the aperture area increases with the square of 1.4, i.e. 2x.. (double the area..)

 

[Thomas78]

...
There is a "German" f-stop series that goes 1.6 - 2.2 - 3.2 - 4.5 - 6.3 - 9 - 12.5 - 18 - 25 - 36. You can find that on older Leica lenses for example.
...

The "German" f-stops series has the number 100 as basis.

100 - 72 - 50 - 36 - 25 - 18 ...

 

[sevo]

Because as some point in time, a major (and popular) manufacturer arbitrarily selected 2, 2.8, etc.

Not really - as others already have pointed out, it is the (area rule doubling) sequence starting from 1.

if you start looking at 19th century and early 20th century lens (esp large format) you'll see all kinds of F stops.

Prior systems were different - quite a few did not have any calculated base relative to light thoughput at all, but were simply sequence numbers or letters.

 

[Roger Hicks]

Because as some point in time, a major (and popular) manufacturer arbitrarily selected 2, 2.8, etc.

if you start looking at 19th century and early 20th century lens (esp large format) you'll see all kinds of F stops.

And it's not a dumb question, rather good one I think,

You can't really call arbitrary to use a system that starts with (or at least includes) 1.

The only three systems that ever achieved much popularity since the 1880s were the current system; the Continental system (typically 1/3 stop slower than the current system, so 2.3 - 3.2 - 4.5 - 6.3 - 9); and (a very poor third) the Uniform System, which never really caught on in its native Britain but was more popular in (appropriately) the U.S. US 1 = f/4, US 2 = f/5.6, US 3 = f/8, etc.

There's been a good deal of fairly arbitrary rounding of maximum apertures, often towards a smaller number for a marketing advantage, with f/3.8 instead of f/4 or f/7.7 instead of f/8, and f/12.5 represented as f/12.3, but in the 20th century, I think that 'all kinds of f/stops) may be a slight exaggeration.

Cheers,

R.

 

[Roger Hicks]

The "German" f-stops series has the number 100 as basis.

100 - 72 - 50 - 36 - 25 - 18 ...

Ah! Wonderful! That makes eminent (if slightly weird) sense. Thanks very much for clearing up a minor puzzle.

Cheers,

R.

 

[DNG]

n5jnr said
Because the f-numbers they refer to are the focal length of the lens divided by the effective diameter of the aperture

Sample

Lens = 100mm

f/1 = 100mm opening of the blades 100mm/1=100mm
f/2 = 50mm opening if the blades 100mm/2=50mm
f/2.8 = 35.7mm opening of the blades 100mm/2.8=35.7mm
f/4 = 25mm opening of the blades 100mm/4=25mm

Lens = 50mm

f/1 = 50mm opening of the blades 50mm/1=50mm
f/2 = 25mm opening of the blades 50mm/2=25mm
f/2.8 = 17.85 opening of the blades 50mm/2.8=17.85mm
f/4 = 12.5mm opening of the blades

NOTE:

n5jnr said
but how much light a circular aperture passes is a function of its area, not its diameter

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.

 

[russelljtdyer]

My Vague Understanding of the Numbers

My Vague Understanding of the Numbers

As I understand it, so that each stop of the aperture scale would mean twice as much light hits the film or image sensor, the aperture or opening relates to 2 (i.e., doubling). I don't quite get the engineering calculations. However, they take the square root of 2 to whatever power along a scale from 0 to 9, generally.

Look at this table of values I've created. I've listed the square root of 2 to each power and the calculation it equals. For those who don't remember their math lessons from school days, I've included the squared value of each 2. For example, 2 to the power of 6, or 2^6 equals 64 (i.e., 2 x 2 x 2 x 2 x 2 x 2 = 64). From there, the square root of that, or √2^6 is the same as √64, which equals 8 (i.e., 8 x 8 = 64). Why all of this translates to doubling, or, depending on the direction of the scale you follow, halving the amount of light on the film or sensor, I'm not sure.

√2^0  =  √1    =   1       -->   f/1
√2^1  =  √2    =   1.41    -->   f/1.4
√2^2  =  √4    =   2       -->   f/2
√2^3  =  √6    =   2.83    -->   f/2.8
√2^4  =  √16   =   4       -->   f/4
√2^5  =  √32   =   5.66    -->   f/5.6
√2^6  =  √64   =   8       -->   f/8
√2^7  =  √128  =   11.31   -->   f/11
√2^8  =  √256  =   16      -->   f/16
√2^9  =  √512  =   22.63   -->   f/22

These calculations gets truncated to one decimal place below f/8, and zero decimal places above f/8--maybe for style or space for the numbers on the scale on the lens.

 

[Muggins]

and (a very poor third) the Uniform System, which never really caught on in its native Britain but was more popular in (appropriately) the U.S. US 1 = f/4, US 2 = f/5.6, US 3 = f/8, etc.

Where does my 1900s Kodak with a scale that goes 4-8-16-32-64-128 fit? I assume it's a similar scale as each number is twice the last, but unless I'm being very dense it doesn't fit any of the schemes already discussed.

Adrian

 

[Sarcophilus Harrisii]

Not being at all familiar with the camera in question, nevertheless it sounds to me much like the lens barrel is only marked for every other stop, as these are otherwise quite "normal" Ie. f/2.8; 4; 5.6; 8; 11; 16; 22; 32; 45; 64 etc. Are there any markings in between those numbers, or, is it possible to set the aperture halfway between them? I'm sure more knowledgeable members can clarify, but this would be my understanding.
Regards,
Brett

 

[Teuthida]

If you've ever had to read Leslie Stroebel's BASIC PHOTOGRAPHIC MATERIALS AND PROCESSESS as part of your photographic education, you would know the answer is this :

aperure numbers depend on two things, the focal length of the lens and the effective aperture, which is the diameter of the entering beam of light that will just fill the opening in the diaphram of a camera.

F numbers are calculated by dividing the lens focal length by the effective aperture. This is obviouslywhy the same aperture will be physically smaller/larger depending upon the focal length of the lens.

 

[Muggins]

Not being at all familiar with the camera in question, nevertheless it sounds to me much like the lens barrel is only marked for every other stop, as these are otherwise quite "normal" Ie. f/2.8; 4; 5.6; 8; 11; 16; 22; 32; 45; 64

That would make perfect sense, Brett, except that the lens is an f8 Rapid Rectilinear*. Looking at Kodak's "standardisation" policy of the time, I don't think that sense comes into it... I don't have the camera to hand, but I think the aperture is continuous, operated by a lever. I ought to measure them, as best I can between the lens elephants, and work out what they actually are and see how they compare to the scale.

Adrian

*http://historiccamera.com/cgi-bin/librarium2/pm.cgi?action=app_display&app=reference&app_id=12&

 

[Beemermark]

You can't really call arbitrary to use a system that starts with (or at least includes) 1.R.

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.

 

[rxmd]

Where does my 1900s Kodak with a scale that goes 4-8-16-32-64-128 fit? I assume it's a similar scale as each number is twice the last, but unless I'm being very dense it doesn't fit any of the schemes already discussed.

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).