Nidelva river through Trondheim Norway

Nidelva river through Trondheim Norway
by Saaru Lindestokke                

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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?

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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. – Ben Crowell Jan 31 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 Clark Feb 1 at 6:44
    
People browsing casually should be warned that the top-voted and accepted answer by ElendilTheTall is incorrect. – Ben Crowell Feb 1 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 Clark Apr 16 at 5:12
up vote 12 down vote accepted

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.

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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 at 14:00
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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 at 14:48
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@scottbb LOL autocorrect. "Non-TOY" – mattdm Jan 31 at 15:13
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@MathematicalOrchid Note focal length but focus distance. – mattdm Jan 31 at 15:15
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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 1 at 1:48

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 Clark Feb 1 at 6:35
    
@MichaelClark: Thanks for the comment. I've edited the answer to reflect this. – Ben Crowell Feb 1 at 16:52

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.

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Sorry, that was an ambiguous wording in my edited paraphrase. I've corrected it. – mattdm Jan 31 at 18:42

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