How do they come up with focal lengths for lenses?

There are a lots of lenses for each camera and I understand that each lens caters to a different use case but my question is on how they arrive at these numbers.

For eg: there are prime lenses which are 50mm, 24mm, 35 mm etc. How do they come up with these numbers? Why dont they have say, 29 mm or 32 mm?

The question holds good for zoom lenses also: on what basis do they determine the start and end focal length of such a lens?

-
For the record they do have odd focal lengths coming out, the Zeiss 55mm comes to mind but in any reference to it Zeiss seems to want to call it a 50mm. –  Peng Tuck Kwok May 9 '13 at 4:05
There are plenty of odd focal-length lenses. Pentax makes a 31, 43, 55 and 77 at least. There are even fractional ones, like the Tokina 16.5-135mm, Nikon 10.5, Sigma 4.5 and Samyang 7.5, so I have no idea where you get your assumptions. –  Itai May 9 '13 at 14:11

First, most "label" focal lengths are approximate, so there may be a 29mm or a 32mm, but it's likely that they will be labelled 28mm and 35mm respectively (or, in this APS-C-is-a-valid-format world, they may both be labelled 30mm). To my knowledge, only a few makers (notably Hasselblad) will state their actual, measured focal length anywhere but on a data sheet hidden in the manual somewhere.

There is a major sequence of lenses that progresses along an approximately square-root-of-two ratio. Not exactly the square root of two, and some of the common focal lengths are inherited from different manufacturer's systems, but close enough for government work, as they say. That includes the 20/21mm, 24mm, 35mm, 50mm, [a gap exists], 100mm, 135mm, 200mm, 300mm, 400mm, 600mm, and 800mm focal lengths. Along that sequence, each lens's field of view varies by about the same proportion from the one preceding and the one following, so if you're stuck with all prime lenses, you can easily determine which one to use when. But there are notable gaps and additions to the sequence. The spot that should be occupied by a 70-ish millimetre lens is occupied by an 85mm in the prime world. That just happens to give a better perspective than anything on the main sequence for people pictures taken with a certain framing, and so it usurped the place of the 70/75mm lens. (The 70mm focal length was resurected for zooms because one doesn't have to forego the 85mm to get it, nor does one have to buy both.) Similarly, the precipitous gap between the "wide normal" 35mm and the undeniably wide-angle 24mm (on a 135-format frame) necessitated an intermediate length, the 28mm.

Macro lenses tended to have a more exact statement of the focal length. The original reason was that so many of the calculations required for magnification and exposure depended on knowing the actual focal length of the lens. (Which is also why there's a film plane indicator on SLRs to this very day.) These days, the stated focal length for a macro lens is a matter of tradition as much as anything else; internal-focus macro lenses will vary their actual focal length, making old-school manual calculations both impossible and irrelevant. Various makers, though, have stuck with their old macro lengths.

Zooms tend to start and stop at familiar focal lengths so that people know more or less what to expect. Crop sensor cameras threw a sort of a monkey wrench (or spanner, if you prefer) into the works, though, at least as far as the old system went. The familiar 18-55mm lens is the near-equivalent (in terms of field of view) of the once-common 28-85mm full-frame zoom, which was itself an upgrade to the older 35-70mm "normal" zoom. (It used to be a fact that a 2:1 zoom would be acceptable, but 3:1 was really pushing it. Optics have come a long way in a short time.) Those crop-sensor equivalents have become familiar signposts as well over the years, so mixes like the 18-105mm or 18-200mm have a meaning to users of crop sensor cameras. But there are oddballs out there as well, like the 17-whatever zoom that can only be intuitively understood as "a little wider than a 28-euivalent but not quite as wide as a 24". With zooms, though, sticking to a sequence isn't nearly as important as it is with primes.

-
Derp! Sorry dude, I missed that altogether. Retracted :) –  NULLZ May 9 '13 at 4:51
The similarity beteen our answers is uncanny. :) I saw your answer come in but didn't read it until I was done. Good point I missed about made-for-APC-C focal lengths — the Pentax 55mm I mentioned really falls under that, and their 16-55mm / 55-135mm f/2.8 zooms are directly meant to compare to "traditional" 24-70mm / 70-200mm. –  mattdm May 9 '13 at 5:54
@mattdm -- a good indication of the simple truth, then. I usually lose these "races", watching "my" answer come in as I'm typing it. We both faied to mention that the "base lens", the 50mm/2", was a cheap, common cine lens with a large-enough image circle that predated the Ur-Leica format and was close enough to "normal" to win by default. (Yours is better organized and laid out, BTW.) –  user2719 May 9 '13 at 7:09

It's tradition. I'm not exactly sure where the tradition comes from, but there is a series of traditional prime lenses for 35mm, and these are still carried on in prime lenses today, and in less likely places: zoom-reflector flashes tend to zoom in a series of big steps matching these focal lengths, and one often finds the same thing with compact camera zooms (lower-end Canon P&S cameras often show this dramatically, with only half a dozen stops).

These are:

• 24mm
• 28mm
• 35mm
• 50mm
• 70mm
• 85mm
• 100mm / 105mm

With the exception of 28mm and 85mm, these roughly follow a sequence on the order of the square root of two, which I don't think is for any magical reason except that it's a decent enough spacing and because hey, we're familiar with that math in photography. As Stan notes in a comment, the starting point in this little sequence is almost certainly 50mm, chosen for convenience as a readily-available existing cinematography lens design when the 35mm film format was invented.

I put the focal lengths in the root-2 sequence in bold; I also put 70mm in italics because despite being in the sequence, for some reason it's a more rare duck in actual prime lenses (but it's still common for flash zoom steps).

These steps tend to be the end of zoom focal length ranges as well. Note that they're mostly rounded to the nearest 5mm, except at the wider end where a single mm makes a big difference in angle of view; it's often the case that the lens's actual focal length is different from the nominal one, but we still call it, for example, a 35mm lens.

There are also notable lenses that aren't in the above list.

My dad's old Minolta came with a 55mm "normal" lens, and Pentax makes a 55mm portrait lens today. Or, there is a popular basic lens design for a very low-profile ("pancake") 40mm lens, available in different designs from Pentax, Voigtlander, and Canon today and in older versions from Nikon and Konica and probably others.

Macro lenses are often 60mm or 90mm. (For whatever reason, SLR primes of these lengths are rarely not macro designs; there may be some appeal in making macro lens not exactly coincide with the focal lengths of lenses people already have? That's speculation.)

And, of course, because they can't resist being odd, Pentax's FA Limited series is 31mm, 43mm, and 77mm. (43mm matching the diagonal of a 35mm film frame, 31mm being sqrt(2) down from that, and 77mm because.... I don't know, but it's a lovely lens.)

-
How is the square root of 2 progression created? The square root of 2 is 1.4 (approx). Where does that fit it here? How do you create the rest of it? 1.4 looks more like an f-stop to me. Sorry if this is obvious. –  legomaker May 9 '13 at 4:50
24mm × √2 ≅ 35mm; 35mm × √2 ≅ 50mm; 50mm × √2 ≅ 70mm. (And 1.4 does look like an f-stop — that's what I meant about this being familiar.) –  mattdm May 9 '13 at 5:03
105mm is another outlier, really; I have no idea why 105 over 100, which is both closer to the √2 pattern and a nice round decimal number. –  mattdm May 9 '13 at 5:06
Surprisingly (or not) f-stops are also a √2 based sequence... 2 x √2 = 2.8, 2.8 x √2 = 4, 4 x √2 =5.6, etc. –  BobT May 9 '13 at 14:18

I have a Helios 44-2, which is 58mm. And also, they round off the numbers. a 17 mm lens may be 17.5 or 16.5, so this is why reviews sometimes compare brands of similar zoom ranges and state that one brand is wider than the other. Choosing a good "Range" or prime focal length is a bit of habit and a bit of knowledge of what makes a comfortable FOV to work with and trade off with zoom range and optical performance. for example Canon 24-70 vs 24-105 L lenses. 24-70 is a comfy range, but 24-105 is a bit more tele, which is even comfier, but it is optically weaker. you also have a cheaper version 28-135mm, which is even weaker optically. This is great working ranges on Full frame. With the introduction of the 1.6 crop sensor digital age, they converted these to 17-50mm / 17-85mm lenses. So there you have those numbers. Similarly for primes you get 50mm standard lenses (much more round number than 45mm. And for crop sensors they had to make 35mm. And they needed some gaps like 50, 85, 100, 135, 200, 300 to make a real difference. The higher you get, the larger the gap should be to see a FOV difference.

-
There was also the Topcor 58mm f/1.4, which I think was reincarnated as the Voigtlander Nokton 58mm. –  coneslayer May 9 '13 at 19:56
I believe they came up with the 58mm lens because they acknowledges that 50mm is a bit too short for portraits and 85mm can be too long in tight spots, so 58mm was the right trade off, where portraits start to look nice and you dont need to step back too far. –  Michael Nielsen May 9 '13 at 20:06
@MichaelNielsen: Why do you say 24-105 will be optically weaker? –  legomaker May 10 '13 at 1:11
zoomfactor = long/short. And higher zoom factor means more compromises, unless there's decades of technology advances between them. In this case the compromise is maximum aperture, and the 24-70 is slightly sharper when stopped down to the same aperture. –  Michael Nielsen May 10 '13 at 6:19