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Why is focal length measured in millimeters?

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8  
What would you expect a length to be measured in? –  Philip Kendall Sep 18 '13 at 11:53
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I see a whole string of questions here: "why are shutter speeds measured in seconds?", "why are camera dimensions measured in inches?". I don't think any of them are particularly insightful though. –  Philip Kendall Sep 18 '13 at 12:52
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@philip The examples you gave are not particularly relevant or useful. But this question is relevant as focal length could be measured in something different and is related to the function of the camera. –  damned truths Sep 18 '13 at 12:58
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One obvious reason is that the scientific world generally (not always) uses SI even in countries like the US and UK where it is not used in otherwise general practice. Lens making is very much science, so no surprise there. –  John Cavan Sep 18 '13 at 13:36
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I see a certain dismissiveness in this thread from some people. I would like to state that I think this is an important "History of photography" question and the comment by @mattdm below is an important addition. So, I would say the true answer is: We settled on mm due to a combination of SI units and convenience in terms of magnitudes though historically different units have been used. (I still see ebay listings for 2.8 cm lenses, and I have to pause and think, what kind of lens is that!) –  Kaushik Ghose Sep 18 '13 at 15:04
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6 Answers 6

up vote 17 down vote accepted

Firstly, distance is used for focal length because it measures the distance between the plane of the lens and the point at which refracted rays meet at a point, when the incident rays were parallel. Below is a simple diagram of a single lens. Note: This is only for convex lenses.

enter image description here

The use of millimetres is simply because it is a scale appropriate for this measurement. i.e. the most extreme lengths don't become numbers that are too large or small for us to comprehend easily. Theoretically any measure of length or distance can be used, but this becomes impractical. For instance a 50mm lens could also be said to be approximately 5.28511705 × 10^-18 light years or 0.0005 Km. Both of those measures are extreme but valid, although not practical.

Why not centimetres? Many lenses have focal lengths that are not whole centimetres, and if possible it is better to represent a number without decimal points, and so mm is a more practical unit. There is almost certainly a historical/traditional reason as well.

Camera lenses work on the same principle as the simple single lens, but include many elements for focusing and telephoto purposes.

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1  
50 mm is also 5*10^8 Ångström, which might be a better counterexample to the light year length than your 0.0005 km because it gives you a positive base-ten exponent. It doesn't have a lot of different digits in it, though, given that 1 mm = 10^7 Å. –  Michael Kjörling Sep 18 '13 at 14:21
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Diverging (concave) lenses also have a focal length, but it's negative, since it measures the distance to the apparent origination point behind the lens that the diverging rays appear to come from. –  Ross Presser Sep 18 '13 at 16:03
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Lenses have been measured in other units, but that was very long ago (mostly 19th century). Most I saw that was not mm was cm. –  Skaperen Sep 20 '13 at 2:49
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Because saying you have a .0002485 furlong lens is a lot more cumbersome than calling the same lens "50 mm".

Focal lengths of common lenses happen to be in the range so that integer mm works well. The numbers don't get rediculously large or small, and 1 mm is less than the accuracy we usually care about, but not overly so. In other words, it's a convenient unit.

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Whilst it is used to express the field of view, the focal length of a lens is an actual distance - the distance at which a focussed image is formed from parallel rays. As such any unit of distance could be used - if you look at really old lenses you'll often find it stated in inches. Most of the world has now adopted the metric system so that is what is used (for the sake of standardization, also most lens manufactures are based in Europe or the far east). They could have chosen centimetres or meters but that would have involved using decimal places.

It just happens that the millimetre is just fine enough to specify all common focal lengths as whole numbers.

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mm is also favoured in most Engineering workshops and design labs instead of cm. –  Unapiedra Sep 18 '13 at 23:58
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The point about appropriateness of unit size is well taken, however, just like fonts are measured in points (which are 1/72 of an inch) focal length could well have been measured in some scaling of an inch that gave similarly well behaved numbers. I think that the use of the millimeter came about because a bunch of early tinkering with photography was done in Europe, specifically in France which had just adopted the metric system and so the early technical people went for mm, rather than some fraction of inches. I have no sources for this conjecture, however.

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Early lenses made in England and the US were measured in inches. –  mattdm Sep 18 '13 at 13:19
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The other logical way to characterize a lens could be by the FOV angle it produces.

We would not longer require to think in "35mm equivalences", but we'd need change the designation of the lens depending on the size of the frame/sensor it's being used on. So it seems that denoting the focal length (in any unit) is more convenient, as it does not change if a lens is used on a medium format, full frame, apsc of 4:3 body.

And we would also need to agree beforehand if the angle is measured horizontally, vertically or diagonally too. And then if we measure it in degrees or radians!

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The world's standard for length used to be given in imperial measure. Rumour has it that the foot used was the length of some king's actual foot was used as the measure. I don't know since that was two years before I was born.

There was not a great array of lenses available when Talbot started his experiments. What few lengths that existed for landscape and portraiture was given in the standard measure of the day: inches. Two inches, three inches, four inches, etc.

As the array of lenses expanded, fractional inch lenses were introduced. Still, the inventory was limited. Lenses were still specified in inches. That's also why the f/ ratio was so handy because it avoided all the horrible artifacts that would result by using imperial measure. The ratio was cleaner and handier.

After the metric system was introduced, it became the indicator for length and the world's manufacturing continued in the new and more convenient metric system. Manufacturing of lenses continues in countries that use the metric system and the result is that the USA is the only country that still uses the arcane system.

That's why we use millimetres, now.

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-1 for a lot of irrelevant grandstanding. F-stops are useful because they normalize the light gathering capability accross various focal lengths, having nothing to do with the units that focal length might have been expressed in. Second, there aren't "horrible artifacts" from using different measurement units, only different scale factors. Metric is convenient because many of the scale factors are multiples of 10, but other scale factors don't introduce artifacts. Third, metric is not more precise than others. 1 inch equals 25.4 mm exactly. Different scale factor, not precision. –  Olin Lathrop Sep 18 '13 at 22:00
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Or you could more accurately say "The USA is the only country that uses either system when one is more appropriate to the specific application than the other." –  Michael Clark Sep 19 '13 at 7:59
    
@OlinLathrop I don't agree. One inch equals 25-1/10 mm. Since when is a fraction (decimal) exact? Check the definition of exact. There are no degrees of Exact. The correct word was, is, and remains precise, indeed. Different. –  Stan Sep 20 '13 at 22:35
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1 inch is exactly 25.4 mm because that is how it is defined by international convention. –  Olin Lathrop Sep 21 '13 at 12:29
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