f-number vs light query?

[snerkler]

I understand the relationship between the focal length of the lens, physical aperture size and it's corresponding f-number, and that (in theory) any lens of a given f-number should allow the same amount of light in, but what is that amount of light, what makes x-amount of light f2, and x-amount of light f2.8 etc and how was it decided?

Just curious

 

[Petrochemist]

In the early days of photography there were a host of different aperture scales. The one that finally caught on is where the focal length of the lens is divided by the diameter of the aperture (at the entrance pupil).
This is what decides the f number (not x-amount of light as that varies with the available light!
A 25mm diameter aperture for a 50mm focal length is F/2, the same aperture on a 100mm lens would be F/4 (note the correct way of showing f-mumbers includes the divided by symbol F/4 is focal length divided by four)

Physics can show that this ratio determines how the image intensity varies with subject intensity. Basically as the focal length doubles the light is gathered from a smaller area - half the diameter of the original field of view - Let this light through an aperture twice the diameter of the original set up & the image brightness is restored.

 

[TimHughes]

T Stop is a variation that is more accurate as it relates to light transmission and used for cinema lenses

 

[myotis]

I understand the relationship between the focal length of the lens, physical aperture size and it's corresponding f-number, and that (in theory) any lens of a given f-number should allow the same amount of light in, but what is that amount of light, what makes x-amount of light f2, and x-amount of light f2.8 etc and how was it decided?

Just curious

It's not so much a measure of an "amount" of light, but a measure of how much of the light reflected from the subject is "stopped" from reaching the film or sensor as it travels through the lens.

The longer the focal length of a lens, the greater the amount of light lost as it travels through the lens to the sensor and by making the iris (aperture) smaller you also reduce the amount of light reaching the sensor.

When you double the distance that light travels through the lens you quarter the intensity of the light reaching the sensor, and when you half the diameter of the aperture you also quarter the amount of light reaching the sensor.

This relationship between focal length and aperture means that by calculating the ratio of focal length to iris size gives you an aperture scale f2, f2.8, f4, f5.6 etc that tells you the amount of light (reflected from the subject) will be stopped from reaching the sensor/film by a known and consistent amount regardless of the lens focal length.

Further to Tim's comment, the f-numbers are simple mathematical calculations and don't take into account how much additional light might be lost to internal reflections or the number of lens elements. For critical purposes these losses are physically measured and instead of an f-number scale, a t-number scale is used.

 

[snerkler]

In the early days of photography there were a host of different aperture scales. The one that finally caught on is where the focal length of the lens is divided by the diameter of the aperture (at the entrance pupil).
This is what decides the f number (not x-amount of light as that varies with the available light!
A 25mm diameter aperture for a 50mm focal length is F/2, the same aperture on a 100mm lens would be F/4 (note the correct way of showing f-mumbers includes the divided by symbol F/4 is focal length divided by four)

Physics can show that this ratio determines how the image intensity varies with subject intensity. Basically as the focal length doubles the light is gathered from a smaller area - half the diameter of the original field of view - Let this light through an aperture twice the diameter of the original set up & the image brightness is restored.

Thanks, the bit in the first paragraph is the bit I understand, however it still doesn’t explain what I’m trying to get at.

For example a 200mm lens with a 100mm aperture is f/2 and an 85mm lens with 42.5mm aperture is also f/2.

So somewhere along the way someone decided that if a lens transmits x-amount of light it’s f/2, if it transmits double this it’s f/1.4 etc. so what was the ‘standard’ where it all started?

Was is simply a case that someone started with a 50mm lens with 25mm aperture, decided this meant it was f/2 and then everything else was calculated from that?

 

[Suvv]

50mm divided by 25mm equals 2
It is as simple as that, focal length divided by the aperture diameter gives the f number

 

[snerkler]

50mm divided by 25mm equals 2
It is as simple as that, focal length divided by the aperture diameter gives the f number

Thanks but you’re not getting what I’m asking

As I said in my initial post I understand all that

 

[Phil V]

If I've understood your question...

Surely the relationship is based on the light transmission. If a lens of whatever focal length allows transmission of 100% of the light, that's obviously F/1, when the transmission is only half the light, that's F/1.4, a quarter of the light is f/2. The lens is 'stopping' 3/4 of the light at f/2, stopping half the light at f/1.4.

Each 'stop' being half the light

And technically these are T stops and not F stops, but generally in photography an F stop is close enough.

 

[the_accidental]

The other point to maybe mention (though obvious?) is a given stop doesn’t transmit a certain amount of light in absolute terms, rather a certain proportion of available light (which is what the above says, but trying to be clear for the op).

One example of lenses that transmit less light that the f number would suggest would be mirror lenses, as the mirror obscures some of the area of the aperture.

 

[myotis]

Thanks, the bit in the first paragraph is the bit I understand, however it still doesn’t explain what I’m trying to get at.

For example a 200mm lens with a 100mm aperture is f/2 and an 85mm lens with 42.5mm aperture is also f/2.

So somewhere along the way someone decided that if a lens transmits x-amount of light it’s f/2, if it transmits double this it’s f/1.4 etc. so what was the ‘standard’ where it all started?

Was is simply a case that someone started with a 50mm lens with 25mm aperture, decided this meant it was f/2 and then everything else was calculated from that?

As I thought I had answered you in my post, I obviously don't understand what you are asking

The standard is how the physics of light works. You could start with any focal length, but it makes sense to base the core series of aperture values on whole numbers, f1, f2, f4, f8, f11

Different lenses have used aperture series based on full stops, half stops and thirds of a stop, but in my experience they always include whole number values

 

[TimHughes]

chatgpt tells us the history is...but this might be made up

The Development of the F-Number​

• Friedrich Voigtländer (1840s): The concept of f-stops can be traced back to Austrian optician Friedrich Voigtländer, who in 1840 introduced the first mathematically calculated photographic lens. This was an important precursor to the idea of measuring aperture relative to focal length.
• John Henry Dallmeyer (Late 19th Century): British lens maker John Henry Dallmeyer was another figure who helped lay the groundwork for standardized lens terminology. His work in optical theory contributed to refining the understanding of lens performance and aperture.

The Modern F-Stop System (Early 20th Century)​

• Carl Zeiss Company (1890s–1900s): The standardized system of f-numbers that we use today was popularized by the German optics company Carl Zeiss in the late 19th century. The Zeiss engineers refined the theory behind aperture control, creating lenses that adhered to a consistent f-stop scale.
• Mathematical Basis: The f-number or f-stop is mathematically defined as the focal length of the lens divided by the diameter of the entrance pupil (aperture). The formula is:
  f/stop=focal lengthaperture diameterf/\text{stop} = \frac{\text{focal length}}{\text{aperture diameter}}f/stop=aperture diameterfocal length
  This formula allows the same aperture ratio to yield the same exposure across lenses with different focal lengths. For example, an f/2 aperture on a 50mm lens has a 25mm opening, while on a 100mm lens, it has a 50mm opening, but both transmit the same amount of light relative to their respective focal lengths.

 

[woof woof]

I understand the relationship between the focal length of the lens, physical aperture size and it's corresponding f-number, and that (in theory) any lens of a given f-number should allow the same amount of light in, but what is that amount of light, what makes x-amount of light f2, and x-amount of light f2.8 etc and how was it decided?

Just curious

I think it's worthwhile to think of the f stop as just a way of deciding the size of the hole that lets the light in and providing the same exposure (hopefully) as other lenses set to the same f stop. Besides the size of the aperture other things affect the light that gets through, the glass and the losses through it and the coatings. If you want a more accurate measurement of the light that gets through T stop is more use. Maybe f stops are near enough for photography, I believe T stops are more useful for cinema use as they may well use different lenses during a scene and will want better consistency of output than f stops may give. This is why we often see T stops on cinema lenses.

I've often thought that cinema lenses might be very nice for photography as they are often made in sets in which the lenses all give a similar look whereas still photography lenses often give a quite different look to other similar lenses from the same manufacturer. I certainly see this with Sony lenses. Cinema lenses are generally more expensive though.

 

[sk66]

F-stop is the mathematical transmission efficiency of a lens; and T stop is the measured efficiency, which better accounts for losses of the elements themselves (absorption/scatter/etc). Obviously, to measure it means that it is a value relative to a known source/input value.

The typically *stated values are:
f/0 passes 100%
f/1 passes 20%
f/1.4 passes 10%
f/2 passes 5%
etc

Each time you double the aperture opening area you double the amount of light transmitted; double the area is 1.4x the diameter and why f stops are 1.4x values (rounded).
(*mathematically it is 11% f/1.4, 6% f/2, etc; and not quite just a simple factor 2)

 

[snerkler]

If I've understood your question...

Surely the relationship is based on the light transmission. If a lens of whatever focal length allows transmission of 100% of the light, that's obviously F/1, when the transmission is only half the light, that's F/1.4, a quarter of the light is f/2. The lens is 'stopping' 3/4 of the light at f/2, stopping half the light at f/1.4.

Each 'stop' being half the light

And technically these are T stops and not F stops, but generally in photography an F stop is close enough.

The other point to maybe mention (though obvious?) is a given stop doesn’t transmit a certain amount of light in absolute terms, rather a certain proportion of available light (which is what the above says, but trying to be clear for the op).

One example of lenses that transmit less light that the f number would suggest would be mirror lenses, as the mirror obscures some of the area of the aperture.

As I thought I had answered you in my post, I obviously don't understand what you are asking

The standard is how the physics of light works. You could start with any focal length, but it makes sense to base the core series of aperture values on whole numbers, f1, f2, f4, f8, f11

Different lenses have used aperture series based on full stops, half stops and thirds of a stop, but in my experience they always include whole number values

chatgpt tells us the history is...but this might be made up

The Development of the F-Number​

• Friedrich Voigtländer (1840s): The concept of f-stops can be traced back to Austrian optician Friedrich Voigtländer, who in 1840 introduced the first mathematically calculated photographic lens. This was an important precursor to the idea of measuring aperture relative to focal length.
• John Henry Dallmeyer (Late 19th Century): British lens maker John Henry Dallmeyer was another figure who helped lay the groundwork for standardized lens terminology. His work in optical theory contributed to refining the understanding of lens performance and aperture.

The Modern F-Stop System (Early 20th Century)​

• Carl Zeiss Company (1890s–1900s): The standardized system of f-numbers that we use today was popularized by the German optics company Carl Zeiss in the late 19th century. The Zeiss engineers refined the theory behind aperture control, creating lenses that adhered to a consistent f-stop scale.
• Mathematical Basis: The f-number or f-stop is mathematically defined as the focal length of the lens divided by the diameter of the entrance pupil (aperture). The formula is:
  f/stop=focal lengthaperture diameterf/\text{stop} = \frac{\text{focal length}}{\text{aperture diameter}}f/stop=aperture diameterfocal length
  This formula allows the same aperture ratio to yield the same exposure across lenses with different focal lengths. For example, an f/2 aperture on a 50mm lens has a 25mm opening, while on a 100mm lens, it has a 50mm opening, but both transmit the same amount of light relative to their respective focal lengths.

I think it's worthwhile to think of the f stop as just a way of deciding the size of the hole that lets the light in and providing the same exposure (hopefully) as other lenses set to the same f stop. Besides the size of the aperture other things affect the light that gets through, the glass and the losses through it and the coatings. If you want a more accurate measurement of the light that gets through T stop is more use. Maybe f stops are near enough for photography, I believe T stops are more useful for cinema use as they may well use different lenses during a scene and will want better consistency of output than f stops may give. This is why we often see T stops on cinema lenses.

I've often thought that cinema lenses might be very nice for photography as they are often made in sets in which the lenses all give a similar look whereas still photography lenses often give a quite different look to other similar lenses from the same manufacturer. I certainly see this with Sony lenses. Cinema lenses are generally more expensive though.

F-stop is the mathematical transmission efficiency of a lens; and T stop is the measured efficiency, which better accounts for losses of the elements themselves (absorption/scatter/etc). Obviously, to measure it means that it is a value relative to a known source/input value.

The typically *stated values are:
f/0 passes 100%
f/1 passes 20%
f/1.4 passes 10%
f/2 passes 5%
etc

Each time you double the aperture opening area you double the amount of light transmitted; double the area is 1.4x the diameter and why f stops are 1.4x values (rounded).
(*mathematically it is 11% f/1.4, 6% f/2, etc; and not quite just a simple factor 2)

Many thanks for all of the answers, Phil V and Sk66's answers in particular were more what I was after, much appreciated. After reading all the replies I guess my original post wasn't clear so my apologies for that.

For clarity I understood how the f-numbers were calculated, i.e. 50/25 = f/2 but this doesn't mean anything in terms of the light passing through. There had to be a 'standard' to determine that to double the light from a 50mm lens with 25mm aperture it needed an aperture of 35.7mm. What I was trying to find out was whether there was originally a 'standard' as to how much light each f-number transmits, for example I didn't know whether there was something similar to the sunny 16 rules such as at ISO 100 f/2 with 10000 lumens the shutter speed needs to be 'x' or whether it's purely a percentage of light transmitted.

This has now been answered in that it's purely a percentage of light transmitted (give or take)

 

[Erty]

One great thing about the f stop method is it let's you get exposure right when you change aperture, shutter speed or ISO in your camera without any difficult maths. All you have to do is count.

Increasing ISO, decreasing shutter speed or opening the aperture (smaller f number) all make the picture brighter. Going the other way makes it darker. Changing any of them by one stop changes brightness the same amount. So if you increase brightness by opening the aperture 1 stop you can change the brightness back again by increasing shutter speed or reducing ISO by 1 stop. Cameras are set up so you can do this by counting clicks on a dial.

 

[snerkler]

One great thing about the f stop method is it let's you get exposure right when you change aperture, shutter speed or ISO in your camera without any difficult maths. All you have to do is count.

Increasing ISO, decreasing shutter speed or opening the aperture (smaller f number) all make the picture brighter. Going the other way makes it darker. Changing any of them by one stop changes brightness the same amount. So if you increase brightness by opening the aperture 1 stop you can change the brightness back again by increasing shutter speed or reducing ISO by 1 stop. Cameras are set up so you can do this by counting clicks on a dial.

Thanks, yes I understand the principles of stops and how they relate to each other

 

[Petrochemist]

For clarity I understood how the f-numbers were calculated, i.e. 50/25 = f/2 but this doesn't mean anything in terms of the light passing through. There had to be a 'standard' to determine that to double the light from a 50mm lens with 25mm aperture it needed an aperture of 35.7mm. What I was trying to find out was whether there was originally a 'standard' as to how much light each f-number transmits, for example I didn't know whether there was something similar to the sunny 16 rules such as at ISO 100 f/2 with 10000 lumens the shutter speed needs to be 'x' or whether it's purely a percentage of light transmitted.

As has been stated above the f-number is NOT based directly on how much light is transmitted. This is typically close to being the same for each f-number but not actually the same due to reflections/scatter/absorption etc. For stills photographic purposes it is nearly always close enough, but not close enough for video/movie if lenses are being changed. T-stops are the numbers that relate to actual transmission, but are not so useful in determining depth of field, hyperfocal point, diffraction limits etc. which vary with the aperture.

F-numbers give an idea of how much light will be transmitted, but it not a precise relationship. An uncoated lens will transmit less light at the same f-stop than a similarly designed lens that is multicoated. Each uncoated air/glass interface losses about 4%of the incident light in reflection, this is drastically reduced with coated lenses & further still with multi coated lenses.
Many modern zooms have more than 10 elements (i.e. often 20+ air glass interfaces) this is enough for uncoated elements to loose more than 50% of the transmitted light, so it's just as well these designs use coated elements!

 

[sk66]

If a lens of whatever focal length allows transmission of 100% of the light, that's obviously F/1

No wonder the Voigtlander 29mm f/0.8 lens is so expensive; it's actually creating light!

F/0 is 100%, but you can't get there.
N= f/D is only an approximation; the actual value is N=1/2NA (*numerical aperture); which is N = 1/[2sin(theta')] (entrance angle) for a lens operating in air (the "1" is the refractive index of the transmission medium (air)), which gives a maximum theoretical f-stop of .05. This limit applies to a well corrected spherical lens design (i.e. a camera lens); other lens designs could theoretically achieve lower values.

*a numerical aperture of 1 is also 100%

 

[Phil V]

No wonder the Voigtlander 29mm f/0.8 lens is so expensive; it's actually creating light!

F/0 is 100%, but you can't get there.
N= f/D is only an approximation; the actual value is N=1/2NA (numerical aperture); which is N = 1/[2sin(theta')] (entrance angle) for a lens operating in air (the "1" is the refractive index of the transmission medium (air)), which gives a maximum theoretical f-stop of .05. This limit applies to a well corrected spherical lens design (i.e. a camera lens); other lens designs could theoretically achieve lower values.

I kinda knew it was impossible for a lens to transmit 100% of the light, but I was trying to keep the concept ‘simple’.

 

[woof woof]

I've recently run into some curious discrepancies with Chinese lenses and I've been surprised how much "things" vary between them and my Voigtlanders but even between my Voigtlander and Sony lenses there is some variation but clearly not as much as with the Chinese lenses some of which are clearly and obviously well out of whack at some apertures to a degree which can't be accounted for by differences in glass, the number of elements or coatings. Testing and comparing has been interesting and not something that occurred to me before and as these things are very rarely mentioned in reviews it looks like it's generally not a big thing.

 

[Garry Edwards]

I've recently run into some curious discrepancies with Chinese lenses and I've been surprised how much "things" vary between them and my Voigtlanders but even between my Voigtlander and Sony lenses there is some variation but clearly not as much as with the Chinese lenses some of which are clearly and obviously well out of whack at some apertures to a degree which can't be accounted for by differences in glass, the number of elements or coatings. Testing and comparing has been interesting and not something that occurred to me before and as these things are very rarely mentioned in reviews it looks like it's generally not a big thing.

I don't know about Chinese lenses, but maybe if there are differences then there could be a similar reason to the "fact" that the old Russian lenses (which in fact were Ukrainian) were stated to have greater depth of field at any stated aperture/distance/format than other lenses from other countries. The reason was simple - they calculated the circle of confusion differently, i.e. they used a lower standard, which increased the "acceptable" dof.

And, if anyone wants to know what a circle of confusion is, it's a group of photographers, sitting in a circle, discussing depth of field

 

[Garry Edwards]

And, on a more serious note, I always use the effective or actual aperture (say 10mm) rather than the f/ number to do a quick dof calculation. In all circumstances, an effective aperture will always produce the same dof as any other lens, and unlike the f/number, is unaffected by the focal length of the lens.

 

[Petrochemist]

N= f/D is only an approximation; the actual value is N=1/2NA (*numerical aperture); which is N = 1/[2sin(theta')] (entrance angle) for a lens operating in air (the "1" is the refractive index of the transmission medium (air)), which gives a maximum theoretical f-stop of .05. This limit applies to a well corrected spherical lens design (i.e. a camera lens); other lens designs could theoretically achieve lower values.

*a numerical aperture of 1 is also 100%

Can you provide a source for that claim?
All the sources I've seen claim focal length / aperture is the definition of f-number. Some fail to state the aperture must be measured at the entrance pupil & so those sources are only approximations.

I think I've seen your N=1/2NA derived from this definition, but it's not a form I find useful.

FWIW the refractive index of air is not quite 1, as it varies with temperature, pressure & humidity. IIRC the refractive index of vacuum is defined as 1.
The difference is certainly small, at STP air has refractive index of about 1.0003

 

[TimHughes]

https://en.wikipedia.org/wiki/F-number seems pretty thorough / nice and geeky - take your pick

 

[Petrochemist]

https://en.wikipedia.org/wiki/F-number seems pretty thorough / nice and geeky - take your pick

Thanks Tim
That's one of many sources that gives N=f/A (and correctly states A is at the entrance pupil)

Its reference to numerical aperture under working f-number gives:



Note the curly equals sign used means approximately equal to.
This applies in cases where the object is not far from the lens - which perhaps explains why I've only met numerical apertures in microscopy.

I would consider books on optics to be more authoritative than Wikipedia, but I can't find anything to dispute in their description.

 

[sk66]

Can you provide a source for that claim?

There's been a few discussions about it (or related) on the DPR photographic science and technology forum where some real geeks hang out; guys like Eric Fossum who invented the CMOS image sensor, Bill Claff (photons for photos), and optical engineers like alanr0 (don't know his real name), among others. This is one that came up with a quick search.

Also this wiki page about numerical aperture (not usually used for photography, but related), and this book by Nakamura.