The rationale behind the focal lengths

[01af]

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For years, I kept wondering why the classical focal lengths are what they are, and why virtually all lens manufacturers are offering the same set of focal lengths for 35-mm-format cameras ... 24 mm, 28 mm, 35 mm, 50 mm, etc. Why no 22 mm lenses ... or 30 mm ... or 32 mm?

 

Today, I finally found the answer ... or so I think.

 

I always knew there must be a pattern—such as 15, 20, 25, 30, 35, 40, 45 ... well, that's a very simple pattern but not the correct one, obviously. Focal lengths don't have equal arithmetic distances. How about equal geometric distances, i. e. a constant factor? Looks better but still not right. In fact, the 'factor' is smaller among the super-wides and greater among the telephotos, i. e. definitely not constant.

 

So what's the pattern? A constant factor in the areas of field-of-view? No. A constant factor in the distances from which a given field-of-view will get captured? No.

 

The answer is more complex than that ... but makes perfect sense when you think of it. 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. In other words, the changes in perspective are constant.

 

According to this definition, a perfect (umm, or near-perfect) line of focal lengths, based on the technical definition for what a normal focal length is—i. e. 43 mm for 35-mm format—would look like this:

 

• 11 mm
  
• 14 mm
  
• 17 mm
  
• 20 mm
  
• 24 mm
  
• 29 mm
  
• 35 mm
  
• 43 mm
  
• 53 mm
  
• 65 mm
  
• 85 mm
  
• 105 mm
  
• 135 mm
  
• 180 mm
  
• 250 mm
  
• 350 mm
  
• 600 mm
  

Doesn't that look familiar, basically? 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? And why are virtually all 50 mm lenses in fact closer to 52 mm than 50 mm proper?

 

Now I feel like a veil has been taken away, and all of sudden I now understand the steps between focal lengths. Sure—not all lens line-ups are following the pattern above exactly. But I think the basic principle is now clearer.

[delander †]

For 35mm cameras dont the chosen focal lengths just emanate from those chosen by Leitz from 1930 onwards, ie 50, 35, 135, 90 etc? Why did Leitz choose these initial focal lengths?

 

Are you sure there is any formula behind their thinking?

 

Jeff

[Double Negative]

In the end it really just comes down to preference, I think. Naturally we're accustomed to the 50mm (or 35mm) being "the normal lens."

 

I wrote an article on it a while back actually; "Choosing Focal Lengths" that goes into it quite a bit.

[adan]

@ Double Negative - You're coming at it from the photographer's end. 01af is coming at it from the manufacturer's end. Why did Leica (or Nikon or Canon) choose to make the lenses they did - which provides the array from which the photographer can then pick, after the fact.

 

@01af - You may be overthinking this. A lot of focal lengths were originally chosen for 35mm photography simply because they were already in use on other formats (with totally different "perspective"), and thus the designs were already calculated. A significant point in an era when every lens had to be hand-calculated (no computers). or for some other reason of historical contingency.

 

E.G., "135" was long in use as a standard lens for 4x5 press cameras. "85" was already in use on the Ermanox roll-film camera.

 

You have to ask why Leica bounced around between 90mm (Elmar), 105mm (Mtn. Elmar), 73mm (Hektor) and 85mm (Summarex) - before finally settling on 90mm as the standard "short-long lens" (until the 75mm Summilux - which isn't on your list).

 

There weren't any "24s" until Nikon's SLR lens in 1968 - prior to that, Contax, Canon and Nikon used "25mm" for their RFs - and Leica ignored that focal length altogether for the first 45 years of the M system. After 1968 - Zeiss stayed with 25 (Contax/Yashica); Canon, Nikon, Minolta/Leica, Pentax all took the 24mm route.

 

Every single focal length from 13mm to 21mm was used by someone from the mid-1950s on.

 

13mm (Nikon)

14mm (Canon)

15mm (Nikon, Zeiss, Leica; Canon fisheye)

16mm (Nikon fisheye)

17mm (Canon FD, now Canon TS EOS, also Tokina at one point, Pentax fisheye)

18mm (Nikon)

19mm (Canon, later Leica)

20mm (Everybody but Leica)

21mm (Zeiss, Leica, Nikon RF and early SLR)

 

That kinda scotches the idea that there is something special about 11, 14, 17, 20 (focal lengths Leica has NEVER used, as it happens)

 

Again:

 

24mm (Nikon and virtually everyone else, at some point)

25mm (also Nikon, and virtually everyone else, at a different point)

28mm (most everybody)

29mm (Zeiss Jena/Pentacon)

 

38-48mm lenses were primarily reserved for fixed-lens 35mm RFs (Canonet, Ricoh, etc.) Leica produced nothing between 35 and 50 (OK, 51-53) for 48 years, until the CL's 40mm Summicron. Even though that is the "normal" focal length for 35mm!

 

Then there is Leica's choice of 75mm - soley because it was the longest focal-length that could handle f/1.4 without covering up the rangefinder.

 

Consider the lenses we've seen from 50(ish)mm on up.

 

55mm (Nikon MF macro)

58mm (Nikon's first "normal" f/1.4 for the F mount, and others)

60mm (Konica f/1.2 M-mount, Leica Macro R, Nikon AF macro)

65mm (Leica Viso macro)

70mm (top end of a sea of zooms, bottom end of another sea of zooms)

73mm (Hektor)

75mm (Leica M, some zooms)

80mm (Leica R)

85mm (Leica Summarex, everyone else)

90mm (Leica M, LTM)

95mm (Canon, on a weird front-element-interchangeable SLR, the EXeeQL)

100mm (Leica macro, Canon in many forms/mounts, Minolta)

105mm (Nikon in many forms, Pentax)

115mm (Canon, for the EXeeQL)

120mm (Pentax)

125mm (Hektor Viso)

135mm (universal)

150mm (Pentax)

 

Erwin Puts went through a similar exercise in his "Lens Compendium" - produced a list of focal lengths with ratio Log 0.025 (6%). 42 focal lengths between 10mm and 1000mm. But at that point, one is basically shooting an arrow at a blank wall and then painting a bullseye around the arrow. You can't miss!

 

I've done my own "lens numerology" over the years. I used ratios of FoV, and liked 7:5:3:1 (20, 28, 50, 135(140)); 7:4:1 (21, 35, 135); 5:3:1 (20, 35, 105 - Nikon days). I tried "add the previous lens" - 15, 20, 35, 55, 90. I tried "ends in 5" - 15, 25, 35, 85.

 

Now I just use 15, 21, 35, 75, 135 (plus 180 and 400). They work great together. But I doubt there is a curve that fits those points very well.

[ho_co]

Leica used to teach in the US "Leica School" that the basic rationale was that the vertical field of view when the camera was held horizontal became (approximately) the horizontal field of view when the next longer lens was substituted.

 

That was when the focal length range was 21, 28, 35, 50, 90, 135.

[TomB_tx]

For early SLR lenses the Asahiflex (first Japanese 35mm SLR) originally had a M37 mount with a 50 f3.5 in 1952, then a 58mm f2.4 lens (preset). They also had an 83mm f1.9 in that mount. Then it became Pentax (M42 mount) with a 55mm f2.2 semiauto or 55 f1.8. Fast lenses were simpler in these longer focal lengths as they could clear the early mirrors without being a retrofocus design. In 64 with the Spotmatic they finally went to a 50mm f1.4, which wouldn't work on the earlier models because the mirrors could hit the rear element at infinity focus. For wide angles they had 15, 17&18mm fisheyes, 20, 24, and 28 in the M42 mount. In Telephoto the M42 lines included the 83, a couple different 85, 100, 105, 120, and of course some 135s and up. Many of these lenses were very good. I still have a 1955 Asahiflex with the M37 mount 58 2.4, and use it at least yearly. I still like the all-mechanical cameras of that era.

This was back when camera companies were Optical companies, and lenses were their main business. Cameras just increased the market for the lenses!

[Jeff S]

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To add complexity, I think it's also the case that many lenses have a 'true' measured focal length that might be different than the stated focal length by up to 5% or so in either direction, e.g., a 50 mm lens might really be a 52 mm lens.

 

If so, then this suggests that focal lengths are as much a function of marketing, habit and mass popularity as opposed to any particularly rigid formula or ratio. Otherwise we'd have all kinds of odd numbers floating about, perhaps the same absent ones that the OP wonders about.

 

Jeff

[Guest #12]

...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...

 

can you please rewrite this; better yet, show your work to get the numbers

[pico]

Andy wrote: There weren't any "24s" until Nikon's SLR lens in 1968

 

And in my experience as an early adopter of that lens - it was not very good at all. Didn't they reformulate it later? I'll bet I still have it in storage and could compare serial numbers.

.

[pico]

To add complexity, I think it's also the case that many lenses have a 'true' measured focal length that might be different than the stated focal length by up to 5% or so in either direction, e.g., a 50 mm lens might really be a 52 mm lens.

 

Is that not why some Leica lenses have a number stamped vertically next to the infinity mark?

 

In my experience with aerial lenses, _all_ of them are measured to exact focal length and so marked somewhere on the lens.

.

[giordano]

In my experience with aerial lenses, _all_ of them are measured to exact focal length and so marked somewhere on the lens.

.

Essential for photogrammetry but not for general photography.

[Guest #12]

Leica used to teach in the US "Leica School" that the basic rationale was that the vertical field of view when the camera was held horizontal became (approximately) the horizontal field of view when the next longer lens was substituted.

 

That was when the focal length range was 21, 28, 35, 50, 90, 135.

 

doesn't seem to work...i.e., what sequence of focal lengths do you get based on 50mm?

[pico]

Essential for photogrammetry but not for general photography.

 

Then what of some Leica lenses with the numbers perpendicular and to the right of the infinity mark? Are they not corrections to the nominal focal length stated on the lens?

 

Such as this: http://www.digoliardi.net/00.jpg

[Jeff S]

Is that not why some Leica lenses have a number stamped vertically next to the infinity mark?

 

Yes, but the fact that many lenses don't have the extra number may just be cosmetic and a function of Leica exterior design, not a reflection of actual focal length. I'll leave it to others more technically oriented, and more familiar with Leica lens specifics, to weigh in. I'm betting, though, that most lenses, even Leica are not to the exact mm. But I'm curious if I'm right or wrong.

 

Jeff

[01af]

You may be overthinking this.

I don't think so. Seriously.

 

 

Every single focal length from 13 mm to 21 mm was used by someone from the mid-1950s on.

Yeah—but never were all of them made by one manufacturer. Each manufacturer had some stepping from one lens to the next. Those who made, for example, an 18 mm lens did not make a 19 mm lens. Minolta, for instance, switched from 21 mm to 20 mm in the late '70s when they introduced their 17 mm but they never made 20 and 21 mm at the same time.

 

 

That kinda scotches the idea that there is something special about 11, 14, 17, 20 ...

You're not getting the point. There is nothing special about these particular numbers. They could just as well be, say, 12, 15, 18, 21. You can shift them around as you wish; the point is the stepping between them. And, of course, all these numbers are rounded.

 

 

Then there is Leica's choice of 75mm—solely because it was the longest focal length that could handle f/1.4 without covering up the rangefinder.

Sure. Exceptions happen. Still, 75 mm makes a lot of sense when you shift from 85 mm to 90 mm and then leave out the 105 mm on the way to 135 mm.

 

You don't need to stick to the pattern with mathmatical precision. But my pattern explains the basic shape of most focal length line-ups better than any other other pattern I came across so far.

 

 

Erwin Puts went through a similar exercise in his "Lens Compendium"—produced a list of focal lengths with ratio Log 0.025 (6 %).

This is in no way "similar". Instead it's the same foolish attempt to come up with a some constant factor that never really works.

 

 

I've done my own "lens numerology" over the years. I used ratios of FoV, and liked 7:5:3:1 (20, 28, 50, 135(140)); 7:4:1 (21, 35, 135); 5:3:1 (20, 35, 105 - Nikon days). I tried "add the previous lens" - 15, 20, 35, 55, 90. I tried "ends in 5" - 15, 25, 35, 85.

(Yawn) And all these numerologies don't work, do they? Mine does.

 

 

Leica used to teach in the US "Leica School" that the basic rationale was that the vertical field of view when the camera was held horizontal became (approximately) the horizontal field of view when the next longer lens was substituted.

Which is nonsense because it just is—again—just a constant factor (3:2, or 1.5×) that simply cannot satisfactorily explain the logic behind the focal lengths. Constant factors are always too big for super-wides and too small in the telephoto range.

[wattsy]

I'd always assumed there was a basic fractal relationship between the common focal lengths but then I haven't given the matter more than a couple of minutes thought.

 

Maybe you will win a Nobel prize for this discovery?

[Guest #12]

...

(Yawn) And all these numerologies don't work, do they? Mine does.

...

 

...your 17 numbers agree nominally with 3 of the lenses in the current lineup. (?)

[zlatkob]

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. In other words, the changes in perspective are constant.

I have to echo #12's request for a better explanation. I'm not understanding this. Is there a formula? How did you arrive at it?

[01af]

Is there a formula?

Actually there's a whole array of formulas.

 

 

How did you arrive at it?

I told you. See above.

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[zlatkob]

• 11 mm
  
• 14 mm
  
• 17 mm
  
• 20 mm
  
• 24 mm
  
• 29 mm
  
• 35 mm
  
• 43 mm
  
• 53 mm
  
• 65 mm
  
• 85 mm
  
• 105 mm
  
• 135 mm
  
• 180 mm
  
• 250 mm
  
• 350 mm
  
• 600 mm
  

Interestingly, Canon currently makes or has made nearly all of those:

14

17 (tilt-shift)

20

24

28

35

50

65 (macro)

85

100

135

180 (macro)

600

And these zooms (including some for APS-C) have similar endpoints:

16-35

20-35

17-40

17-55

17-85

24-85

28-135

55-250

35-350