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I've been searching for some confirmation regarding the difference in DEFINITION of Focal length between:

  1. Physics/Optics(Which in the simplest case uses a classical thin lens to define the focal length as the distance from the lens to the focal point/convergence point)

vs

  1. Photography(Which defines it as the distance from focal point/convergence point to the sensor).

Now I understand that a camera is actually a complex assembly of multiple lens elements and I believe this is where I'm getting mixed up.

Is it that since there are multiple lenses we really can't define it in a classical physics thin lens definition way since which lens element are we calculating the distance from?? Thus, instead we calculate from the final convergence point(since there can even be multiple convergence points along the way) to the sensor?? Would I be right in saying this??

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    There are a number of statements in your question which are in error. Perhaps you could just ask how photography defines focal length, because neither of your descriptions is correct for either field.
    – Michael C
    Dec 25, 2020 at 17:32
  • Your question also uses several ambiguous terms. For example, the focal point and the convergence point, both properly defined, are not the same thing in photography.
    – Michael C
    Dec 25, 2020 at 17:35
  • What are the definitions then??
    – ayazasker
    Dec 25, 2020 at 17:38
  • By what standard? Photography or physics? Convergence point can be a bit ambiguous, because some people us it to describe one thing, and other folks use it to describe another thing. Same thing with focal point. Can you describe (for each term separately) what you mean when you use each term? It's very unclear what you man by them in the question. Until we can understand what you mean when you say "convergence point" or "focus point' it's hard to answer your question and say , "yes, you're correct" or "no, you're incorrect.
    – Michael C
    Dec 25, 2020 at 17:50
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    In the answer I linked, I say, "When a lens with multiple elements is used, focal length is measured from the point a theoretical single thin lens would be located having the same refractive properties as the combined multiple elements have." This point can be either in front of the front element of the lens (i.e a telephoto lens), behind the rear element of the lens (i.e. retrofocus), or anywhere between those two points. But where that point is located is not the same thing as where everything "crosses over" inside a lens, which is what some people mean by "convergence point"...
    – Michael C
    Dec 25, 2020 at 18:29

3 Answers 3

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In both physics and photography, the focal length of a converging lens is defined as the distance from the thin lens to the point were collimated light striking the lens will converge into focus. Collimated light is defined as rays that are all originating from the same point that is at infinity from the lens and arriving at the front of the lens parallel to each other.

If the point from which the light rays are originating is closer than infinity, then the rays from that point will not strike the lens parallel to one another. Such rays will also not converge into focus at the lens' focal length, which is always defined based on where collimated light from a point source at infinity converges. In such a case, the distance between the lens and the imaging plane (film/sensor) will need to be greater than the lens' focal length. The closer to the lens the object that we want to focus upon is, the longer the distance between the lens and the image/film/sensor plane needs to be.

When a lens with multiple elements is used, focal length is measured from the point a theoretical single thin lens would be located having the same refractive properties as the combined multiple elements have. This point can be either in front of the front element of the lens (i.e. a telephoto lens), behind the rear element of the lens (i.e. retrofocus lens), or anywhere between those two points.

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  • Michael I think I finally figured it out thanks to your clarification yesterday. Just as you said in both physics and photography the focal length is defined as the distance between the convergence point(i.e the point where all the rays from all points on an object "cross-over" and hence go on to form an upside down image, in a single thin lens this is usually the center of a lens) to the point where all the collimated rays from each single object point unite at their respective focal points on a focal plane.
    – ayazasker
    Dec 26, 2020 at 16:21
  • The ray tracing diagrams online are indeed confusing in that some pictures are showing the "cross-over" point and in others they are showing the focal point and a newbie could easily get mixed up. I would also like to use this example picture we used before to see if I got the gist of what you are saying. vision-doctor.com/images/stories/optik/grundlagen/… in this picture the "Focal length" is the distance when the rays come from infinity, but would it be right to say that the "image distance" is the "focal length if object was closer than infinity"??
    – ayazasker
    Dec 26, 2020 at 16:27
  • Finally, another picture to show the confusion that a newbie can come across. cameraharmony.com/wp-content/uploads/2020/03/… when looking at this picture what we are seeing at the lens is the "cross-over point" correct? Someone who would look at the image I posted in the above comment and then look at this one could easily get confused and ponder why there is no crossover in the first picture whereas there is in the 2nd one?? Did I get the gist of it down? I hope so.
    – ayazasker
    Dec 26, 2020 at 16:33
  • Sorry sorry my bad I realise now that it's the distance from the OPTICAL CENTER OF A LENS(which in the case of a single thin lens is literally the center of the lens itself) to the point where all the collimating rays unite(focal point). Which begs the question then what is the Optical Center of a Lens??
    – ayazasker
    Dec 26, 2020 at 20:14
  • @ayazasker The two different diagrams are showing two different things. The first is showing multiple rays from the same point. The second is showing a single ray (each) from multiple points. "Convergence point" is a dangerous term to use in these discussions because it is far too easy for different people to misunderstand what the other means when they use the term. If one means the center of the lens, then say "center of the lens". If one means where rays from a single point are focused, say the "point of focus."
    – Michael C
    Dec 27, 2020 at 3:17
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There really is no difference between Physics and Photography. The distinction revolves around exactly what you are talking about.

The Focal Length of a Lens is the image formation distance or focal point distance (although it's not really a point) for an object at infinite distance. The infinite distance is another way of stating collimated light.

The Focal Length Used to take a picture will be longer than the lens infinity focal length when the object is closer.

In All Cases the film or sensor is at the Focal Length Used in order to form a sharp image on the sensor. Remember that although the line drawings give the impression of a dimensionless focal point, it's not a point it's an image.

This is my favorite diagram for showing this:

Focus

At (f) the Focal Length Used is also the Focal Length of the Lens.

At (e) which is nearly all photography, the focal length to produce the image is longer than the Focal Length of the Lens. This also explains why there is a close focusing limit for a lens, you eventually can't get it far enough away to place the focus point (image) on the sensor. This is why extension tubes allow you to focus closer than the lens normally allows.

At (d) you enter the official definition of Macro Photography, an image as large as the object.

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  • Note that (b) and (f) are the same thing, just depending on which side of the lens the object and image plane are placed. Also note that (c) and (e) are the same thing as well. That's why "reversing" a lens designed for taking images of things that are beyond 2F allows us to take "macro" images of things between F and 2F.
    – Michael C
    Dec 26, 2020 at 2:43
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    I'd suggest not using the phrase, "focal length used". Just reserve focal length as the inherent lens property, and use subject distance and image distance to describe the related distances on either side of the lens that are described by the thin lens formula.
    – scottbb
    Dec 26, 2020 at 18:11
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As you know, lens aberrations deface the camera image. To mitigate we must construct the lens using an array of several individual lens elements. Some of these elements will have positive power (convex figure). Some will have negative power (concave figure). Some will be air-spaced. Some will be cemented to its neighbor. Try as we might, residual aberration persists. Nevertheless the camera is capable to make spectacular images.

By definition, the focal length is that distance from lens to the focused image, when imaging a far distant object. In other words, an object at an infinite distance (infinity ∞). Because the lens has laminations as to how much refractive power it has, when an object is closer than ∞, we must elongate the distance, object to focused plane. We do this by mechanically moving the lens array. This elongated projection distance is called the “back focus”. Often this distance is incorrectly mentioned as “focal length”.

To find the actual focal length of a complex lens, we put it on an optical bench. We run a series of tests. We find two cardinal points. These are called the front and rear nodal points. The object distance is measured, object to front node. The focal length is focused image distance to the rear nodal. This test is preformed when imaging and object at ∞.

You need to know that the location of the front and rear nodal points can be manipulated by the lens maker. A true telephoto has a shorter barrel because the rear nodal is shifted forward. This makes a long focal length lens less awkward. A wide-angle has the rear nodal shifted to provide clearance for the reflex mirror and its movement. In some telephoto designs, the rear nodal can fall in the air, forward of the camera lens.

A tip of the hat to those who design our lenses.

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