F1.4 F2.8 F5.6 F11 ... Why?

I guess this must be a centry old question, my apology if it

has already been answered before.

 

Here is the question:

My understanding is, F1, F2, F4, F8, F16, F22 are all one-stop

difference, F4 is one stop slower than F2, so logacially the

half stops should be F1.5, F3, F6, F12, F19 ...

 

So why people use F1.4, F2.8 F5.6 instead?

The sequence you cite aren't one stop differences, they're two stops. A one-stop sequence is 1.4, 2.0, 2.8, 4, 5.6, 8.

 

It's a "square root of two" progression, based on area of a circle, Pi*R squared.

Your series is wrong, full stops are: F1.0, F1.4, F2.0, F2.8, F4.0, F5.6, F8.0, F11, F16, F22, F32, ...

f/1 f/2 f/4 f/8 are two-stops - they represent the (optical) diameter of the aperture. The light that goes through the aperture is divided by 4 when you divide the diameter of the aperture by 2 (the area of the aperture is divided by 4). 1.4 is (approximately) the square root of 2, it's the amount that you need to divide the aperture diameter by to divide is area by 2.

Eric, you're thinking linear progression where a shift between 4 and 8, or between 8 and 16, is all you need to halve or double the final product.

 

In controlling light through a lens, the vital parameter is the area (not the linear radius or diameter) of the circle through which light is allowed to pass. To halve or double the light getting to your film, you must halve or double the AREA (again not the linear diameter or radius) of the aperture.

 

However, the f-stop numbers don't refer directly to the area of that circle; they refer to the linear measure of its diameter (or radius) as compared to the focal length of the lens. The term f/2 means the diameter of the aperture is 1/2 the focal length of the lens; f/4 means the diameter of the aperture is 1/4 the focal length and so on.

 

As already mentioned in this discussion, the area of that circle is given by the radius, squared, times the constant pi.

 

So, if you have a nice fast lens at f/2 and you want to cut the light in half to achieve a one-stop reduction in light coming through the lens, you want to make the AREA of the aperture one-half what it was at f/2. You don't want to make the DIAMETER of the aperture half what it was.

 

So you wind up with a new radius that works out to approximately f/2.8 (your former aperture's diameter times the square root of two) which creates a circle with half the area of an f/2 circle.

 

To get a two-stop reduction, you need to halve the area and then halve it again, or in other words you need one-quarter the original area for your aperture... and so the f-stop changes by the square root of 4, not the square root of 2... and voila, the square root of four is (all together now) our old friend 2, which is why two stops from f/2 is f/4... or two stops from f/2.8 is (multiply by 2, carry the 1, watch the decimal...) f/5.6... or why two stops from f/4 is f/8 and so on and so forth.

 

Anyway, it really is just the difference between linear and area calculations that makes it seem counterintuitive at first.

 

Hope that helps. It's really simple. Only took me something like 20 years to figure it out, but I'm thick. If I have explained this incorrectly, someone here will step in and thrash me with a wet noodle.

 

Be well,

As already answsered, and it's f not F<br>f as in f stop, F actually denotes focal length.

OK I guess its actually f/ if you want to get technical :)

Wouldn't it then actually be F/, since F is focal length and f is really F/f? So it's f or F/ but

sometimes f/, what's on second, I don't know's on third....

This appears to be incorrect! Pi are round! Cake are square!

But pizza comes both ways!

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Thanks guys!

I applied the theory, You guys are right, it is the AREA that

matters, and F2.8 is just an approximation, it is actually F2.8284

F5.6 is F5.6569

 

Well, one assumption though, the aperture is round? Most Nikkor

lens are hexagon.

 

Now, time for pizza ... round or square, why not hexagon?

doesn't matter ;)

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Well, photographers never really were matematicians, and that might just be good for all of us. Imagine if we had the f-stops to ten decimals engraved on the lens barrels.

 

Jim, I think it was a very good explanation (hiding the wet noodle until next time ;-)

Eric: yes, f/2.8 doesn't mean "a round aperture that has a diameter of f/2.8" but rather "an aperture that has the same area as a round aperture which would have a diameter of f/2.8".

 

The extra decimals don't matter much, if you compare to the tolerances in e.g. shutter speeds. 10% of tolerance is less than 1/6 of a stop. Notice how the "traditional" shutter values aren't exactly powers of 2.

 

Notice also that having the aperture expressed as a diameter is interesting when doing flash photography. The illumination from a flash (or any other light source for that matters) grows inversely proportionally to the square of the distance, i.e. for a proper exposure the product of the f-stop and distance is a constant (for a given flash/film combo), and that's the "guide number" that's in teh spec sheet for the flash.

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Just one correction, Jean.

the "traditional" shutter values are exactly powers of 2,

e.g. 1/15 is actually 1/16, 1/30 is actually 1/32 and 1/60 is

1/64 so on ... The 1/15, 1/30 and 1/60 is just easier for

people to read.

 

This is great, I can't belive I ask this question almost 20 years

after I got my first camera.

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Eric - exactly my point - it doesn't bother anybody that the "marked" speeds are only approximate, and that they are off by several percent from the theoretical speeds - the 1% error on f/2.8 is small in comparison, and both those errors are small in comparison to the real-world precision of shutters (and that's without talking about leaf shutters that could end up having different speeds at the center and edge).

Eric,

 

You are correct, lens apertures are not perfect circles, more like octagons (or whatever-gons). Applying the formula for the area of a circle to the aperture of a real world lens implies you are approximating the aperture by a circle. It's close enough.

 

You might be an engineer if you assume a horse is a sphere in order to make the math easier...

Hey guys ,,does anyone know what the letter F stands for???? I do know ,,but when everyone starts talking about F-stops maybe first they should know what the F means....It will help to know why the stops are there in the first place.......Rmac

Roy: Focal length. f/5.6 means that the optical diameter of the aperture is equal to the focal length divided by 5.6.

That's not the right answere. What does F stand for.???

Roy - if you know the right answer, feel free to share it with us instead of asking. A century and a half of photography have caused people to sometimes forget the meaning of some of the terms they use.

Roy... there is no agreement on the derivation of the f, sorry.

 

Some say it stands for finestra or fenestra, from our Italian friends' "window" as in the window through which all the light arrives to make the exposure.

 

Some say is stands for "factor" or "factorial," (with the proponents of the former having a stronger case), a reference to the division inherent in a ratio of two linear dimensions: focal length and aperture diameter.

 

Some say Ansel Adams just made it up because he thought "f.64" sounded better than "U.S.256" as a moniker for his group of photographer pals.

 

I do not know of a truly authoritative source that can crown any of those contenders king to the detriment of the simple, logical and widely held belief that the "f" in "f-stop" or "f/stop" stands for the focal length against which the aperture diameter is compared to determine the "stop" in use.

 

Be well,

Stop comes from the fact that an aperture "stops" some of the light. (re Waterhouse Stops.)

 

The Relative Aperture should be indicated by the lower case: f, not F.

The proper way is to show the R.A. is f/#. For example, f/8 means that the diameter of the entrance pupil is equal to the focal length (f) divided by 8.