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I was under the impression that the “focal length” of a lens is the distance at which stuff appears in-focus. (E.g., perhaps I set the camera so that objects 3 meters away appear sharp, and anything nearer or further than that is blurry.) But everything I've read seems to suggest that focal length is actually a slightly odd way of describing the field of view of the lens, and actually nothing to do with focus at all. (?)

So what's the correct term for “stuff at this distance will be in focus” then? (I.e., the thing you change with the focus ring.) If I want stuff 3 meters away to appear sharp, what parameter have I set to 3 meters?

mattdm
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MathematicalOrchid
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    everything I've read seems to suggest that focal length is actually a slightly odd way of describing the field of view of the lens The focal length of a lens is only indirectly related to its field of view. The focal length of a lens is defined by the thin lens equation, and it can be interpreted as a measure of the inverse strength of the lens. If you make a lens's optical surfaces more strongly curved, or if you increase its index of refraction, it gets stronger, and the focal length goes down. –  Jan 31 '16 at 20:10
  • Field of view has absolutely nothing to do with focal length until it is combined with the size of the projected image. (i.e. sensor size or film size). A 50mm lens is ultra-wide angle on a large format camera, wide angle on a medium format, normal on a 35mm/FF camera, slightly telephoto on an APS-C or µ4/3 camera, and super telephoto on a camera with a 1/3" or smaller sensor. – Michael C Feb 01 '16 at 06:44
  • People browsing casually should be warned that the top-voted and accepted answer by ElendilTheTall is incorrect. –  Feb 01 '16 at 16:55
  • It is correct enough within the constraints of still photography in the same way that Newton's laws of motion are correct enough within the constraints of velocities well below the speed of light, Einstein's General and Special Theories of Relativity notwithstanding. – Michael C Apr 16 '16 at 05:12

3 Answers3

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Focal length is the distance between the lens and the sensor when the subject is in focus, not the distance to the subject.

The term for the distance to the subject in focus is the focus distance and is measured from the image plane (sensor/film plane). The distance from the lens to the subject is called the working distance which can be significantly less within the context of macro photography. The zone which appears in focus either side (front and back) of the subject is the depth of field. This varies with the aperture - depth of field increases as the aperture gets smaller (f-number gets larger). All else being equal, depth of field is greater at f/4 than at f/2.

So if you focus on an object 3 meters away with a focal length of 18mm and aperture of f/11, everything from 1m to infinity will be in focus. However, if you focus on the same subject with the same aperture with a focal length of 135mm, the near focus limit is 2.9m and the far focus limit is 3.1m - the depth of field is only 20cm deep, in other words.

Michael C
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ElendilTheTall
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    +1, but a couple of important clarifications. First, in a complex lens (like any non-toxic camera lens) , the point from which one measures focal length is complicated — and not to be confused with the flange focal distance. And second, note that the nominal focal length of a lens (the one written in the specs and on the lens) is that of the lens focused at infinity. – mattdm Jan 31 '16 at 14:00
  • "Focal length" ≠ "focal distance"? Oh my God, those sound like exact synonyms! Damn, that's confusing… – MathematicalOrchid Jan 31 '16 at 14:08
  • @mattdm "non-toxic"? – scottbb Jan 31 '16 at 14:30
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    Another (minor but important) clarification: Depth of field is not the zone that is "in focus"; it is the zone that appears "acceptably in focus". Only one distance is "perfectly" in focus, regardless of the aperture setting. (What appears in focus in an image also depends on at least the enlargement and viewing distance of the final image.) – osullic Jan 31 '16 at 14:48
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    @scottbb LOL autocorrect. "Non-TOY" – mattdm Jan 31 '16 at 15:13
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    @MathematicalOrchid Note focal length but focus distance. – mattdm Jan 31 '16 at 15:15
  • The aperture gets smaller when the f-number gets larger, because the f-number is a divisor. The physical aperture at f/4 is smaller than at f/2, for the same value of f (focal length), because a quarter of something is less than a half of the same thing. The depth of field grows larger when the physical aperture grows smaller (larger f-number), however. I have proposed an edit to correct this in the answer. – user Jan 31 '16 at 16:42
  • Focal length is the distance between the lens and the sensor when the subject is in focus, No, this is wrong. Check any freshman physics textbook. The distance you're defining is called the object distance, and it is always greater than the focal length (for a real image, which is the case of interest for photography). –  Jan 31 '16 at 20:16
  • My head still hurts from that brief but intense pondering of how this toxicity-complexity trade-off might work... o.O – junkyardsparkle Feb 01 '16 at 00:39
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    @BenCrowell In photography, the given definition is acceptably accurate. A lens's nominal "focal length" is that for an object at infinity, and, further, is generally only an approximation for objects at a distance >> (actual) focal length. In these limits, the definition holds. Given their ability to focus at all, even prime lenses naturally cannot have an absolutely fixed focal length (per a physicist), but again, this definition is acceptably correct in the context at hand. If you're happy to accept that Newton has his place when Einstein is "more correct", so too can you see this as true. – J... Feb 01 '16 at 01:48
  • Very discouraging that the top-voted and accepted answer is simply wrong. This is simple freshman physics. (And BTW I have a PhD in physics and have been teaching the subject for 20 years.) –  Feb 01 '16 at 16:54
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    @BenCrowell It is not wrong. How can you have a PhD in physics and yet fail to appreciate that equations, definitions, and theories are defined within a given set of limits? With object distance u and image distance v, focal length f is 1/f = 1/v + 1/u. In a camera, 1/u <<1/v and so focal length is f ≈ v. These types of approximate equations are so shockingly common in all branches of physics that I wonder what it is you are teaching your students. By your logic, Newton's laws of motion are "simply wrong", notwithstanding that the entire world uses them just fine for v << c – J... Feb 10 '16 at 01:01
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    @BenCrowell Of course, you could argue that even 1/f = 1/v + 1/u is "simply wrong" since it is an approximation of a thin lens, and a photographic lens is certainly not that at all. 23 lens elements in 19 groups... better break out Zemax for that one. This answer should probably be at least a few chapters long before anyone dares hazard a notion about what a focal length actually means. ;) – J... Feb 10 '16 at 01:15
  • @BenCrowell The same nomenclature often means different things in different disciplines. This is true even when the disciplines are related. Calling the plane where the film or sensor resides the "focal plane" is totally incorrect in laboratory physics. Yet the world's largest manufacturers of cameras (Canon and Nikon) both label the sensor/film plane as the "focal plane." A shutter with curtains directly in front of the film/sensor plane has always been called a "focal plane shutter." – Michael C Dec 17 '17 at 11:10
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The thin lens equation is 1/f = 1/do + 1/di, where

  • f = focal length
  • di = image distance = distance from lens to sensor
  • do = object distance = distance from lens to subject.

The focal length of a lens is defined by the thin lens equation, and it can be interpreted as a measure of the inverse strength of the lens. If you make a lens's optical surfaces more strongly curved, or if you increase its index of refraction, it gets stronger, and the focal length goes down. When you change do and di so as to maintain focus, the focal length f normally stays constant; this is what justifies interpreting it as a fixed property of the lens. (As pointed out in a comment, some lenses do contain moving parts that allow them to automatically change their focal length, but this is a side issue.)

So what's the correct term for “stuff at this distance will be in focus” then?

Generically, in optics, this is called the object distance. In photography it can also be referred to as the focal distance.

everything I've read seems to suggest that focal length is actually a slightly odd way of describing the field of view of the lens

Not really. Focal length just happens to be related to the magnification and field of view.

A possible source of confusion is that in many cases when you're doing photography, do is much greater than di. Under these conditions, di is approximately the same as f. Therefore some people may be under the impression that the focal length is defined as the distance from lens to sensor. But in reality, when you change the focus on your camera, di changes while f stays the same.

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    Most lenses used for still photography demonstrate focus breathing to one extent or another. When you change the focus on the lens the focal length of the lens does change, as does the field of view. Some lenses demonstrate this more than others. For example the Canon EF 70-200mm f/2.8 L IS II exhibits very little focus breathing. At 200mm and MFD the actual focal length is still near 195mm. The Nikon 70-200mm f/2.8 VR when set at 200mm and focused at MFD the actual focal length is only about 140mm and the field of view is similarly larger than when the lens is focused on infinity. – Michael C Feb 01 '16 at 06:35
  • @MichaelClark: Thanks for the comment. I've edited the answer to reflect this. –  Feb 01 '16 at 16:52
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The specific answer to the core of your Title Question, "the term for the distance", is: Infinity. Infinity is the (imagined) subject distance in front of the optical center of the lens that corresponds to an in-focus image on the sensor when it is spaced behind the lens at the nominal focal length. The engraved "focal length" which appears somewhere on the lens housing is a hypothetical specification of the nominal distance from the lens to the sensor when (imagined) subjects at infinity appear "in-focus" on the sensor. For a simple axi-symmetric double convex lens, the measuring reference point is the optical center (also called the geometric center) of the lens. To focus images of real subjects closer than infinity, the lens must be moved away from the sensor, towards the subject. In this situation, the focus (not focal) distance is always longer than that number engraved on the barrel (the focal distance). Thus, the nominal focal length is a convenient label to characterize the focus properties of the lens assembly. For compound lens assemblies there is no easily found reference point. The reference point is the center of a hypothetical single element with the same focal length. In this case the technique to determine the reference point is very complicated. It is up to the reader to investigate further. In answer your second question regarding: “stuff at this distance will be in focus”, the term is "subject to lens distance". Given f = focal length, u = subject to lens distance, and v = sensor to lens distance, the following formula represents the relationship: 1/f = ( 1/u ) + ( 1/v ). At infinity, 1/u approaches zero.

sidjones
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