The rationale behind the focal lengths

[zlatkob]

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I told you. See above.

Well, that's a big help. All clear now.

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[earleygallery]

Such trivialities aren't that important when it comes to creating images, we use what we have don't we?

[lct]

...Didn't you sometimes feel that the usual line of 35—50—85 (or 35—50—90) is missing something, because the steps between any two focal lengths are pretty close, except those around 50 mm?...

35/50/90 has always been my favorite combo with FF but i prefer 28/50 with APS-C and 28/35/50 with APS-H. Sounds pretty subjective to me.

[earleygallery]

35/50/90 has always been my favorite combo with FF but i prefer 28/50 with APS-C and 28/35/50 with APS-H. Sounds pretty subjective to me.

 

Indeed, most important of all is how the individual photographer sees.

[Wallyvision]

Speaking of perspective; James' comment puts all this blather into the proper one. As for the more technical use of the term referred to in this thread; perspective is not changed by a change in focal length. Only field of view is changed, the perspective remains the same if the camera doesn't move.

[Jeff S]

As for the more technical use of the term referred to in this thread; perspective is not changed by a change in focal length. Only field of view is changed, the perspective remains the same if the camera doesn't move.

 

True, but the OP already took that into account using his approach.

 

Jeff

[Wallyvision]

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Jeff: Apologies if I misread the original post but in referring to the magnification of various focal lengths he does state: "In other words, the changes in perspective are constant." You will have to excuse the interpretive capabilities of an old man.

[Sp12]

35/50/90 has always been my favorite combo with FF but i prefer 28/50 with APS-C and 28/35/50 with APS-H. Sounds pretty subjective to me.

 

Interestingly, my choice is 28 or 31, 60 or 65, and 100 on FF.

[Jeff S]

Jeff: Apologies if I misread the original post but in referring to the magnification of various focal lengths he does state: "In other words, the changes in perspective are constant." You will have to excuse the interpretive capabilities of an old man.

 

No problem, from one old man to another. The operative phrase precedes your quoted sentence and says "there's a constant factor in the magnifications of the background when shooting from various distances..." That's why he refers to "changes in perspective." At least that's my interpretation, which doesn't make it necessarily correct.

 

Jeff

[adan]

"Between the 'classical' focal lengths, there's a constant factor (cum grano salis) in the magnifications of the background when shooting from various distances that will get constant magnification in the plane of focus. Sounds more complex than it actually is."

 

I think I'm getting your intended point: that if you photograph, say, a person's head with various lenses, such that the head is always the same size (constant magnification in the plane of focus) in the various pictures, then the size of a building in the background will change according to some "constant factor".

 

OK - what is the "constant factor?" Can THAT be expressed as a single number, ratio, equation, or sequence of numbers?

 

Does your theory allow the prediction of the next number below 11, and the next number above 600?

[pico]

[...]

I think I'm getting your intended point: that if you photograph, say, a person's head with various lenses, such that the head is always the same size (constant magnification in the plane of focus) in the various pictures, then the size of a building in the background will change according to some "constant factor".

 

I cine work it's called a dolly zoom. The subject stays the same size as the dolly moves in, maintains focus on the principle object, retains its size, and at the same time zooms out. I'm sure you have seen it. See the link for the formula belo.

 

From Wikipedia: To achieve the effect the camera needs to be positioned at a certain distance from the object that is supposed to remain still during the dolly zoom. The distance depends on how wide the scene is to be filmed, and on the field of view (FOV) of the camera lens. Before calculating the distances needed at the different fields of view, the constant width of the scene has to be calculated. For example, a FOV of 90° and a distance of two meters yield a constant width of four meters, allowing a four-meter-wide object to remain still inside the frame during the effect

 

 

I would not worry about it - or practice it, either.

And still photographers think their job is difficult.

[01af]

Between the 'classical' focal lengths, there's a constant factor (cum grano salis) in the magnifications of the background when shooting from various distances that will get constant magnification in the plane of focus. [...]

I think I'm getting your intended point: that if you photograph, say, a person's head with various lenses, such that the head is always the same size (constant magnification in the plane of focus) in the various pictures, then the size of a building in the background will change according to some "constant factor".

Exactly.

 

 

OK—what is the "constant factor?" Can THAT be expressed as a single number, ratio, equation, or sequence of numbers?

As a single number, of course—that's the whole point. Otherwise it wouldn't be constant. In principle, it could be any positive number (well, except 1). To make practical sense, it should be a number greater than one but smaller than two. A factor of two or greater would translate to very large steps between focal lengths.

 

As it turns out, for the typical 35-mm-format lens line-ups, the intended factor seems to be the fourth root of two, that is, 1.1892.

 

 

Does your theory allow the prediction of the next number below 11, and the next number above 600?

The next numbers below 11 would be 10, then 8. However they are badly rounded and hence, rather inaccurate. The actual numbers are more like 11.5, 9.6, and 8. The next number after 600 would be 1,300, and then, infinity. The sequence of constant perspective changes cannot be continued ad infinitum; it naturally comes to an end as soon as the factor between the magnifications of the foreground and background becomes equal to or smaller than our intended factor (1.1892). Of course you can always use a still longer focal length, and you will get a still bigger background magnification—but the factors between the background magnifications will become smaller and smaller from one focal length to the next, no matter how long your telephoto lens.

 

That's the reason why there's an upper end in lens line-ups. When you are in the ballpark of, say, 1,000 mm (for 35-mm format) then using a still longer lens (from a longer distance) won't make any perceptible difference in perspective anymore. If you shoot a landscape detail from one mile away with a 1,000 mm lens and then the same detail from four miles away with a 4,000 mm lens then the pictures won't be significantly different ... except that getting good image quality across four miles will be even harder than across one mile (camera shake, wind, haze, air motion)—but that's not my point here.

 

Sure—lenses longer than 600, 800, or 1,000 mm for 35-mm format do exist. But they are rare and unwieldy, and their sole purpose is to reach out into the distance, e. g. for shooting wildlife. They don't serve any purpose in terms of perspective change for image composition, as the shorter lenses do. So unless you utterly need to capture a certain subject across a certain distance, it does not make sense to own telephoto lenses that are longer than 300 - 600 mm (for 35-mm format). If you have one lens in that focal length range then you're all set. In terms of perspective, longer lenses than that don't make any useful difference.

[Erik Gunst Lund]

Interesting reading!

You must keep the Fish Eyes; 4.5 and 8mm circular image and 10.5 and 16mm for Full Frame Fish Eye lenses separate from the rectilinear lenses out of this 'equation'

Since there the Focal Length is chosen from the projected image size and the projection type chosen.

[01af]

It just occurs to me that maybe I shouldn't use the word 'factor' ... maybe 'ratio' would be better? I am using these two words as if they were synonyms.

 

Consider a small number x, a bigger number X, and y := X/x, then these equations hold:

 

1. X/x = y
   
2. x/X = 1/y
   
3. x * y = X
   
4. X/y = x
   

Would you—the native English speakers—call y a factor or a ratio? In eq. 1 it's the latter; in eq. 3 it's the former ... so I don't see much of a difference between these two terms. Do you?

 

 

You must keep the [...] Fish Eye lenses separate from the rectilinear lenses out of this 'equation'.

No-one ever mentioned fish-eye lenses ... so why do you?

[Jeff S]

It just occurs to me that maybe I shouldn't use the word 'factor' ... maybe 'ratio' would be better? I am using these two words as if they were synonyms.

 

Consider a small number x, a bigger number X, and y := X/x, then these equations hold:

 

1. X/x = y
   
2. x/X = 1/y
   
3. x * y = X
   
4. X/y = x
   

Would you—the native English speakers—call y a factor or a ratio? In eq. 1 it's the latter; in eq. 3 it's the former ... so I don't see much of a difference between these two terms. Do you?

 

 

It has been a while since basic math, but I think a ratio would be more correctly expressed as X:x (relative proportion), whereas division of X/x yields a quotient of y. But, yes, in the third equation, x and y are factors of X.

 

Jeff

[Guest #12]

...

 

Consider a small number x, a bigger number X, and y := X/x, then these equations hold:

 

1. X/x = y
   
2. x/X = 1/y
   
3. x * y = X
   
4. X/y = x
   

...

 

you don't even have this right...so I would still want to see your calculations

[lars_bergquist]

The real rationale behind just about every focal length is that someone is already making it. Which means that some people demand it.

 

The slightly defocused old man

[Guest #12]

the camera system I use has a 45, 65, and 135, which I'm sure were off-the-shelf designs...the 135 was recalled and replaced with a 100, which had nothing to do with spacing between focal lengths.

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[Erik Gunst Lund]

16mm (Nikon fisheye)

 

Well the fish eye lenses where mentioned...

 

But dont bother with that....

[Manolo Laguillo]

Hi,

 

perhaps I've missed it, but I think nobody mentions another possibility, the 3 dimensions of the film:

short side (a), long side (, diagonal ©

 

These dimensions give the three basic focal lenghts:

 

a = is a "really wide" wide angle

b = is a moderate wide angle

c = is the "normal" focal length

 

In 35mm films that's 24, 36, 42

 

In 4x5 inches film that's 90, 120, 150

 

In 6x6, which is in reality more or less 5,5 x 5,5, the short side is 50mm and the long side 60mm

 

 

Making 2x or x/2 give the rest:

 

24 x 2 = aprox 50

36 x 2 = aprox 75

42 x 2 = aprox 90

 

42 : 2 = 21

36 : 2 = 18

24 : 2 = 12

 

Because ± 1 mm in the wide angle section is a lot, but negligible in the tele section, we can round up 36 to 35, 42 to 40, and 48 to 50

 

So we have this progression:

 

12, 18, 21, 24, 35, 40, 50, 75, 90

 

NB: as you can see, I don't go in the nuances between a 24 and a 25mm... :-)

 

Conclusions:

with 24x36, the 28 mm is a strange focal length, and the 50 mm too

 

but... the 50 mm is interesting, because it allows 2 things:

 

1. making shoulder portraits without being too close to the person photographed (too close means problems with the perspective: protruding eyes)

2. making group pictures without being too far away (a big distance means problems in the communication between the photographer and the group being photographed)

 

It's odd that the 40mm made for the CL had a short life, because in other formats that's the normal lens: in 6x6 a 75/80mm is like a 40mm in 24x36, and in 6x9 that's the 90mm. I'm thinking in the magnificent 6x9 Fuji.

 

...

 

Therefore we could speak of a "sociology of the focal lengths": the city behind the work of Cartier-Bresson (mainly 50mm) is not the same as the city of Gary Winogrand (mainly 28mm) or the city of William Klein (21mm).

 

Exceptions do exist, of course: Robert Doisneau speaks of Atget (someone belonging to one generation older than HCB's) using with 18x24 plates the aequivalent of a 18mm in 35mm, if memory does not fail me.

 

The "rationale" is, in any case, the use the photographers make of their tools. Fashions and trends play a very important role here, of course.