Physics/Optics vs Photography definition of focal length

Question

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

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

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??

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 '20 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 '20 at 17:35
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 '20 at 17:50
For the physics definition this is what I was using as a reference https://www.google.com/search?q=focal+length&client=tablet-android-asus-tpin&prmd=ivn&sxsrf=ALeKk03TUof_DXvlzHl5KfIrx2ho53WHww:1608918645810&source=lnms&tbm=isch&sa=X&ved=2ahUKEwiq_euC2entAhVPzqQKHUL4DlMQ_AUoAXoECBcQAQ&biw=768&bih=1024&dpr=2#imgrc=mL9hE1m3o70CpM — ayazasker, Dec 25 '20 at 17:53
The problem with using the term convergence point is that it means one thing when looking at a ray diagram that shows light from a single point striking all points on the front of a lens and then converging at the image plane. It means an entirely different thing when looking at ray diagrams that show the limits of a field of view that converge at the thin lens and then expand back out to the edges of the focal plane (as defined in photography). — Michael C, Dec 25 '20 at 17:53
Where is "focal point/convergence point" on any of the drawings at the results of that google search? You realize two different google searches don't return the same results for the same search terms, depending on the user's browser history and other data collected by google for each individual user? — Michael C, Dec 25 '20 at 17:56
As for the Photography definition of Focal length It's basically almost every definition I find online which always mentions that it's the distance from Convergence point to the Sensor. Now as to what specific Convergence point they are talking about I really couldn't say(I just always assumed it's where all the light rays from each point on an object converged after passing through the lens) — ayazasker, Dec 25 '20 at 17:59
My bad this picture should clarify what I meant for the physics definition https://www.vision-doctor.com/images/stories/optik/grundlagen/Optical_path_biconvex_lens.png — ayazasker, Dec 25 '20 at 18:00
Your definition of focal length in photography as the distance from the convergence point behind the lens (defined by physics as the rear focal plane) to the sensor is incorrect. See this answer to the related question linked in an above comment. — Michael C, Dec 25 '20 at 18:06
Where is the article that drawing is a part of? It's not correct as photography uses those terms. — Michael C, Dec 25 '20 at 18:07
I think part of your problem is that you aren't making a distinction between diagrams that show collimated rays from a single point at infinity striking different points on the surface of a lens from multiple rays from the same point at a distance less than infinity that strike the lens at different points on the surface of the lens. Collimated rays converge behind the lens at the focal length of the lens. Rays from a closer object are not collimated and will strike the front of the lens at different angles, and will converge at a distance different than the lens' focal length. — Michael C, Dec 25 '20 at 18:18
In the "this answer" post you referred me to the 1st answer says "Focal length is the distance from the conversion point to the image plane. The image plane could be film, or a digital sensor". As to your statement "the focal length is the dimension labeled as image distance a' in that drawing" I've read on multiple sources that the distance is not necessarily from a lense but rather the CONVERGENCE POINT(which seems to be the misunderstanding of our convo) which isn't necessarily on the lens element in complicated lens assemblies. — ayazasker, Dec 25 '20 at 18:19
That's why the term "conversion point" (not even "convergence") is a bad one to use in such an ambiguous manner. It's not clear to you, the reader what the writer of that answer meant when he said "conversion point." — Michael C, Dec 25 '20 at 18:22
"I've read on multiple sources that the distance is not necessarily from a lense but rather the CONVERGENCE POINT(which seems to be the misunderstanding of our convo) which isn't necessarily on the lens element in complicated lens assemblies." This is because you're not making the distinction between objects located at infinity in which all the rays from said object arrive at the lens parallel to one another (i.e. collimated) and objects that are closer to the lens and those rays arrive non-collimated. — Michael C, Dec 25 '20 at 18:25
If an object is closer than infinity to the lens, the rays will not converge at the lens' focal length — Michael C, Dec 25 '20 at 18:25
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 '20 at 18:29
... That is, the point where light from all points converges as it crosses over in the lens between the location of the theoretical thin lens and the image plane.. — Michael C, Dec 25 '20 at 18:31
In this diagram you linked above, it is assumed the object is closer to the lens than infinity. If the object were at infinity, f' and a' would be the same distance. — Michael C, Dec 25 '20 at 18:35
Aaah I believe I understand what you are getting at!! That is the 2 different definitions of convergence. 1) which would be defined as the convergence of all light rays from a single point allowing for focus vs 2) all light rays from all points on an object which "cross-over" to give an upside down image. Am I on the right track?? — ayazasker, Dec 25 '20 at 18:39
Ok then allow me to reconsider my framework/terminology so that I can reword my question better. — ayazasker, Dec 25 '20 at 18:51
Does this diagram start to make sense about how various rays converge at different places? — Michael C, Dec 25 '20 at 18:53
Rays at different points that are all parallel to the optical axis of the lens all converge at F'. Rays at different points that all go through the lens at its optical center all converge at the lens (where they pass through the optical center). Rays at different points that all converge at F will be parallel after they pass through the lens. — Michael C, Dec 25 '20 at 18:56

score 3 · Accepted Answer · answered Dec 26 '20 at 02:37

3

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.

answered Dec 26 '20 at 02:37

Michael C

175,039
10
209
561

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 '20 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. https://www.vision-doctor.com/images/stories/optik/grundlagen/Optical_path_biconvex_lens.png 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 '20 at 16:27
Finally, another picture to show the confusion that a newbie can come across. https://cameraharmony.com/wp-content/uploads/2020/03/focal-length-graphic-1-1024x539.png 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 '20 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 '20 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 '20 at 03:17
@ayazasker "... would it be right to say that the "image distance" is the "focal length if object was closer than infinity"?" No. The focal length of the lens does not change (unless it is a zoom lens and the relationship between various elements change). The image distance is the image distance, but the focal length of the lens does not change. What has changed is that the object we desire to be in focus is closer and we need to move the image distance away from the lens (in actuality, we usually move the lens forward to increase the distance between lens and sensor) to bring the closer... – Michael C Dec 27 '20 at 03:21
... object into focus. But in so doing, objects at infinity are now not in focus at the image plane. They're still in focus at the focal length behind the lens, but nothing is recording them there. – Michael C Dec 27 '20 at 03:23
@ Michael C - A true telephoto, as compared to its long-lens cousin, has a foreshortened barrel length, This arrangement makes the telephoto less awkward. This is accomplished by a set of converging lenses followed by a set of diverging lenses that reduce the convergence. This design shifts the rear nodal point forward. In some designs it may even fall in air forward of the front most glass element. The distance, rear nodal point to the focused image of an object at an infinite distance, is measured, this becomes the published focal length. Back-focus is last glass to focused image. – Alan Marcus Dec 31 '20 at 16:55
@AlanMarcus Which is what I succinctly said with, "... This point can be either in front of the front element of the lens (i.e. a telephoto lens)..." – Michael C Jan 03 '21 at 08:41
Regarding the last paragraph, what is this theoretical point called? (The point where the theoretical single thin lens that summarizes the whole lens setup would be.) Is this the "optical center"? – Anakhand Oct 26 '22 at 11:16

score 2 · Answer 2 · answered Dec 26 '20 at 02:10

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:

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.

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 '20 at 02:43
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 '20 at 18:11

score 1 · Answer 3 · answered Dec 26 '20 at 07:10

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.

Physics/Optics vs Photography definition of focal length

3 Answers3