Help with F-Stops and exposure

[wiltw]

Thank you all for great responses!

I do understand most of this, and I get that the f/stop number is related to the area/geometric property and has a log(2) relationship.

I guess what I'm getting out of this is as follows:

Full f/stop values go in the sequence: f/1.0 f/1.4, f/2, f2.8. This scale is standard because it begins at 1.

However my lens *clicks* at f/1.8, f/2.8, f4 ... and so on. This means that the difference between the first and second click is in excess of one f/stop

This means that if I go from the first to the second *click* I'm closing the aperture slightly more than a stop, and slowing the shutter by one stop will not result in the exact same exposure, so the rule of clicking the aperture and shutter in opposite directions but keeping exposure identical is not a correct assumption between the first two clicks on my lens because they are more than a stop. (Though probably not enough to get upset about)

What you say is true, but then from a practical standpoint

• often the engraved f/stop is not the true f/stop, as magazine tests from decades past prove
• unless you are shooting color transparency, variances in exposure are masked by enlarging and test prints made to determine right number of seconds of enlarger light
• we may see variances in the accuracy of shutter speeds, which add to or compensate for variances in f/stop

For instance in various tests by Popular Photograph

• an OM f/2 lens was truly f/2.06
• an OM f/2.8 lens was truly f/2.73
• an OM f/3.5 lens was truly f/3.29

and Modern Photography found in several examples of OM 50mm f/1.8 lens

• two samples were really f/1.86
• one sample was really f/1.87

IOW, you worry about exact difference when reality is that few lenses are really exactly as engraved, even at the engraved usual 'full f/stop values', and shutter speeds are often not exactly as engraved either!
"Polishing a turd" comes to mind.

 

[Chan Tran]

What you say is true, but then from a practical standpoint

• often the engraved f/stop is not the true f/stop, as magazine tests from decades past prove
• unless you are shooting color transparency, variances in exposure are masked by enlarging and test prints made to determine right number of seconds of enlarger light
• we may see variances in the accuracy of shutter speeds, which add to or compensate for variances in f/stop

For instance in various tests by Popular Photograph

• an OM f/2 lens was truly f/2.06
• an OM f/2.8 lens was truly f/2.73
• an OM f/3.5 lens was truly f/3.29

and Modern Photography found in several examples of OM 50mm f/1.8 lens

• two samples were really f/1.86
• one sample was really f/1.87

IOW, you worry about exact difference when reality is that few lenses are really exactly as engraved, even at the engraved usual 'full f/stop values', and shutter speeds are often not exactly as engraved either!
"Polishing a turd" comes to mind.

All of your listed value are within the value of 1 decimal point except the f/3.29 for f/3.5.

 

[Dali]

This means that if I go from the first to the second *click* I'm closing the aperture slightly more than a stop, and slowing the shutter by one stop will not result in the exact same exposure, so the rule of clicking the aperture and shutter in opposite directions but keeping exposure identical is not a correct assumption between the first two clicks on my lens because they are more than a stop. (Though probably not enough to get upset about)

The rule you are makeing reference to is valiid in theory if you can change thr aperture by +/- 1 full stop. Otherwise, you cannot fully compensate the aperture change with the shutter (unless you shoot AUTO)..

In reality, it does not really matter as it is unlikely you accurately master exposure + developement. As someonesaid earlier, any small exposure deviation can be compensated under the enlarger.

 

[wiltw]

All of your listed value are within the value of 1 decimal point except the f/3.29 for f/3.5.

My point was the engraved value typically is not the actual value...even when it is within manufacturing tolerance.

OP is correct...if all shots were exposed in a single contact sheet, the f/1.8 shot would be a bit brighter, if you had incrementally altered shutter speed by 1EV for each -1EV change of click-stop of the lens (assuming lens with only full stop click positions) AND assuming all f/stops and shutter speeds were as marked!

 

[AgX]

However my lens *clicks* at f/1.8, f/2.8, f4 ... and so on. This means that the difference between the first and second click is in excess of one f/stop

That is interesting. I assumed that your lens, as for instance my FD lens, still got an unmarked half stop at F2.4 (as I described in post #14).

 

[spl]

That is interesting. I assumed that your lens, as for instance my FD lens, still got an unmarked half stop at F2.4 (as I described in post #14).

No, it doesn't, and there isn't room for it, I checked carefully. It's the cheerful Zukio Auto-s 50mm that may have come stock with the OM-1 way back when.

 

[AgX]

Thank you for raising this topic. I was aware of the irregularity seen at some lenses between the first two clickstops, but not to this extent.

 

[CMoore]

I understand what you guys are saying, but i am not able to follow the math.
A lens aperture is the area of the lens that is exposed by the blades...isn't it.?
To double the area of a circle... a lens aperture.. you do not multiply by 2...you multiply by the square root of 2, is that correct.?

 

[wiltw]

I understand what you guys are saying, but i am not able to follow the math.
A lens aperture is the area of the lens that is exposed by the blades...isn't it.?
To double the area of a circle... a lens aperture.. you do not multiply by 2...you multiply by the square root of 2, is that correct.?

Which is how you get the f/stop progression for whole f/stops (some rounding error embedded in the numbers) 1, 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22

 

[CMoore]

Which is how you get the f/stop progression for whole f/stops (some rounding error embedded in the numbers) 1, 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22

Yes...Thank You.
Although f/stops are weird because they are fractions so i guess the opposite math would apply.?
To show half the area, you would multiple by sq2 f8 to f11
To double the area you would divide by sq2 f11 to f8

 

[MattKing]

I understand what you guys are saying, but i am not able to follow the math.
A lens aperture is the area of the lens that is exposed by the blades...isn't it.?
To double the area of a circle... a lens aperture.. you do not multiply by 2...you multiply by the square root of 2, is that correct.?

The area = pi x the radius of the aperture squared.
To double the area, yes you multiply the radius of the aperture by the square root of 2, because then when you square the new radius the area becomes twice what the area was first.
To add complexity, the f/stop is the ratio of the diameter of the aperture and the focal length. And of course the diameter is twice the radius.

 

[CMoore]

The area = pi x the radius of the aperture squared.
To double the area, yes you multiply the radius of the aperture by the square root of 2, because then when you square the new radius the area becomes twice what the area was first.
To add complexity, the f/stop is the ratio of the diameter of the aperture and the focal length. And of course the diameter is twice the radius.

Right.
I had forgotten that.
Looking back it is mentioned at the beginning of this thread......or it is mentioned in a link at the beginning of this thread.
I am NO Math Whiz. But i do think that the ratio of focal length to the diameter of the aperture is important to learn, at least once.
I am sure ALL Photographers ask their teacher why is f/11 half of f/8. Why isn't it f/16.?
It is an intuitive question, especially for people like myself that never had Geomoerty

 

[spl]

I am NO Math Whiz. But i do think that the ratio of focal length to the diameter of the aperture is important to learn, at least once.

Here is my very amateur maths take on the reasoning for the scale being logarithmic:

I suppose if F-stops were a relationship between area and focal length they may make more sense to students, because the scale would then be linear and 16 would be double 8 and thus let in twice the light and be one stop up. However because F-stop is defined as the relationship of diameter to focal length this happens:

FOCAL LENGTH / DIAMETER <- square/log2 relationship to -> AREA <- linear relationship to -> LIGHT ON FILM

The square relationship between the Diameter and Area is because of the equation: Area = pi * r^2

If we just talked about area then we would have a linear relationship to light, and then 16 would be double 8 etc. However if we talk about area then we leave focal length out of the equation and then our numbers are different for every lens! That means every lens would have a different scale that the camera/photographer has to have a lookup table for!

So to model the difference between lenses we introduce the focal length by relating the Focal Length / Diameter to the light hitting the film, so we no longer worry about area thus we have:

FOCAL LENGTH / DIAMETER <- square/log2 relationship to -> LIGHT ON FILM

So we get a logarithmic scale that confuses photography students, but it works over different focal lengths and lenses which helps greatly in the long run.

One final note: This is doubly important for zoom lenses because as you turn the zoom ring the focal length of the lens changes, so if you try to use an area to light relationship then your F-stop scale would change too as you zoom, which is just crazy and unusable. The logarithmic scale makes the standard F-stop scale the same for every focal length and every setting of every zoom lens, which is useful.

 

[AgX]

I understand what you guys are saying, but i am not able to follow the math.
A lens aperture is the area of the lens that is exposed by the blades...isn't it.?
To double the area of a circle... a lens aperture.. you do not multiply by 2...you multiply by the square root of 2, is that correct.?

Some fellows want to understand the mathematical background behind apertures, transmission charts etc. And often it is even a prerequisite for the interpration of for instance charts.

However concerning apertures, for the practitioner it should be sufficent to know of the factors 1.4, 1.2 and 1.1 for establishing a 1, 1/2 and 1/3 stop change at aperture values.

 

[wiltw]

Yes...Thank You.
Although f/stops are weird because they are fractions so i guess the opposite math would apply.?
To show half the area, you would multiple by sq2 f8 to f11
To double the area you would divide by sq2 f11 to f8

Larger f/number = existing f/number * 1.414 (or existing f/number /0.707)
Smaller f/fnumber = existing f/numr * 0.707 (or existing f/number / 1.414)

 

[beemermark]

A simple answer with reference to the lens in question: the lens does offer 1.8, but then not enough room to inscribe f2 between 1.8 and 2.8. The 1.8 probably is a promotional ploy. Many of my lenses marked f2 actually open up slightly more...probably to 1.8, but who would ever need the tiny difference? As others have commented, just consider the 1.8 to be read as 2. Most high end lens makers wouldn’t bother.

Correct answer. Making faster lenses is a marketing gimmick. Difference between whole stops is meaningful, fractional stops less so. So my camera has a lens with f2.0, competitor comes out with a lens marked f1.8, next competitor ups the ante with a f1.7 lens. Don;t overthink it.

 

[MattKing]

Correct answer. Making faster lenses is a marketing gimmick. Difference between whole stops is meaningful, fractional stops less so. So my camera has a lens with f2.0, competitor comes out with a lens marked f1.8, next competitor ups the ante with a f1.7 lens. Don;t overthink it.

Note however that you probably don't want to label your f/1.8 lens as an f/2.0 lens, because that will screw up some things related to slide film.

 

[AgX]

Correct answer. Making faster lenses is a marketing gimmick. Difference between whole stops is meaningful, fractional stops less so. So my camera has a lens with f2.0, competitor comes out with a lens marked f1.8, next competitor ups the ante with a f1.7 lens. Don;t overthink it.

Exactly. I never understood why a F1.2 lens was called a necessity for 35mm low light photography, when about every serious photographer had a F1.4 lens in house.

 

[AgX]

Thank you for raising this topic. I was aware of the irregularity seen at some lenses between the first two clickstops, but not to this extent.

Well, I got a lens where the gap between the first two clickstops is 1 1/2 stops...
(It is a F 1.2 lens.)