# Why are lenses characterized by focal length and not the effective field of view?

In photography, it's the accepted norm to say that if you know the sensor size of your camera and the focal length of your lens, then you know the field of view of your system.

However, in optics, it's well known that for a fixed sensor size, the distance from the lens to the image plane (which we can equate with the flange distance) also affects your field of view. Everyone who mounted his\her lens on a macro adapter had seen that increasing the flange distance will narrow down your field of view, and they will end up with a macro lens.

So my question is why do we characterize lenses with the focal length and not the effective field of view?

I realize that it could be the case that it was just an arbitrary historical decision, but I'm curious whether there's justification for that which I'm missing.

EDIT:

I want to make a few things clear in light of some of the comments I got.

From the physics POV of it all, what determines the effective FOV for a given sensor is the effective focal length of the lens and the distance between the back principal plane of the lens to the sensor, which is determined unambiguously by the distance between the principal plane and the flange of the lens plus the distance between the flange of the camera and the sensor.

These two properties are completely independent of each other, but changing either of them will change the effective FOV - this is a fact of geometrical optics.

My question was: given that both parameters affect the FOV, why is it then that we attribute only the focal length to the FOV of the lens?

To further clarify by an example: you can have a 50mm and a 40mm lenses both with the same distance between the principal plane and the flange of the lens. In this case, if you place the 40mm lens sufficiently further from the sensor (compared to the 50mm lens) you will have the same effective FOV.

Please try to answer my original question instead of trying to educate me about optics - that part of the conversation I got down pretty good :)

• "... the distance from the lens to the image plane (which we can equate with the flange distance)..." is not correct. the same optical formula can place the same lens elements the same distance from the imaging plane regardless of the registration distance. Assume a 200mm simple lens. The ffd can be 20mm and the lens barrel 180mm long, or the ffd can be 100mm and the lens barrel 100mm long. Both add up to 200mm. Oct 29, 2018 at 1:40
• Related: Why is focal length measured in millimeters? The comments and answers discuss the difference between focal length and FoV. Oct 29, 2018 at 1:53
• @YuvalWeissler How can a 50 and a 40 mm lens, focused at infinity have the same field of view? Oct 29, 2018 at 10:02
• @YuvalWeissler Your lack of any basics is confusing you. Angle of view is 2 arc tan (field dimension / distance * 2). The angle of view is also 2 arc tan (sensor dimension / focal length * 2). These are equal angles and similar triangles and equal ratios. One can be computed from the other. What is totally false is : "an optical designer can in principle design a 40mm lens that will focus at infinity and also have the same FOV as a 50mm lens on a given sensor." Simple geometry strongly disagrees. An adapter might convert one, but that then would have result of equal focal lengths. Oct 29, 2018 at 17:40
• Possible duplicate of Why do we talk about focal-length when frame sizes are different? Aug 17, 2019 at 2:07

This question is predicated on a misconception. The flange distance is included in the focal length in lens labels — it is the distance from the optical center of the lens focused at infinity to the imaging medium. This includes the flange distance. (See What is the reference point that the focal length of a lens is calculated from?, and What exactly is focal length when there is also flange focal distance?)

This means that for a given sensor size, lenses made for different mounts are still comparable — a 24mm lens gives (approximately) the same field of view regardless of the mount distance of any given system. So, focal length does correspond to field of view.

You note that using a macro adapter affects field of view. In fact, they also increase the focal length, although since macro extension tubes remove the ability to actually focus at infinity, we leave practical reality and get into the realm of theory.

• In photography, lenses are marketed and sold as I have described. You are right that they are independent, but lenses are made and sold for a particular mount, and that means the flange focal distance of that mount is included in the number on the lens. Oct 28, 2018 at 10:25
• This means that a 24mm lens on Pentax K mount will have approximately the same field of view as a 24mm lens for Canon or Nikon or whatever else, assuming the same sensor size. Oct 28, 2018 at 10:26
• @YuvalWeissler Again, the focal length of a complex lens is measured when that lens is focused at infinity. If you change the distance from the lens to the sensor, you will need to change the focus in order to make the focal plane coincide (that is "not have everything be all blurry"). This is true from "the physics point of view" and from any other point of view. Oct 28, 2018 at 14:19
• @YuvalWeissler "... which will result in any distance one wishs between the back principle plane of the lens and the sensor (which we can equate to the flange distance)." Your assumption is false. The back principal plane of a lens is not necessarily located at the ffd. Sometime it can be quite a bit in front of the ffd (many telephoto lenses), sometimes it can actually be behind the ffp with lens elements that protrude into the light box. Oct 29, 2018 at 1:44
• "... the flange distance dictates the distance between the lens' principal plane to the sensor." No it does not. You can have a lens with 200mm between the principal plane and the sensor regardless of whether the ffd is 10mm or 100mm. Beyond absurd extremes (such as designing an 8mm lens for a format with a ffd of 200mm), flange distance in no way dictates the focal length of a lens. Oct 29, 2018 at 6:48

Focal length and lens FOV are inherently the same thing. The variable is how much of the lens' FOV is utilized (i.e. extension tubes/TC's/crop sensor/etc). Why would you specify a lens' characteristic by something that may be variable?

• Well, not exactly. One 50mm lens, say, for an 8x10 LF camera will project a much larger image circle with a much wider FoV than another 50mm lens, say, for a µ4/3 camera, that projects a smaller image circle with a narrower FoV. The center 22mm of the large image circle will show the same thing as the entire 22mm image circle of the smaller lens. The rest of the much larger image circle will show things outside the FoV of the smaller lens. Oct 29, 2018 at 2:25
• Yes, but in reality the FOV seen by the the two lenses are the same. It's simply that the lens designed for the smaller sensor crops the FOV (smaller image circle) because the sensor it's designed for cannot utilize all of it.... and because it's cheaper/easier. Oct 29, 2018 at 3:53
• Another way to think of it is, the 50mm LF lens is still a 50mm lens when mounted on m4/3... only the smaller sensor doesn't utilize all of the image circle. The only difference between it and a 50mm m4/3 lens is that the m4/3 lens discards the excess FOV and projects a smaller "usable" portion of the FOV. Oct 29, 2018 at 4:02
• No. Two lenses can have the exact same focal length and the front element of one can collect light from a wider angle of view and refract that light from a wider angle of view into the lens while the other does not collect light from as wide an angle of view and refract it down into the lens. Oct 29, 2018 at 4:14
• Not without some physical limitation imposed... i.e. designed for a smaller image circle/sensor. FOV of a lens w/o imposed limitation is simply the magnification/enlargement vs distance from the scene. Perhaps it is simpler to separate FL as magnification and FOV/effective FOV (which is image circle/sensor dependent) Oct 30, 2018 at 3:45

So my question is why do we characterize lenses with the focal length and not the effective field of view?

The very good reason for cameras is that field of view also strongly depends on the sensor size. A small sensor captures a more narrow view than a larger sensor can.

The lens focal length does provide some field of view, which the sensor size crops to capture possibly a lesser amount of it. Cameras with tiny sensors only capture a small field, so they have to use a much shorter focal length lens to compare to an expected "regular picture" view seen by other cameras with larger sensors. Crop Factor compares that sensor size view to the historical 35 mm film frame size view that so many of us are very familiar with.

Focal length is NOT at all about the mounting flange distance. The internal focus node can be moved by design. A "telephoto" lens means that node is slightly in front of the front lens element (lens is shorter than the focal length). A retro-focus (wide angle) lens places that focus node behind the rear element, to create space behind the lens. But focal length is to that focal node.

The focal length marked on the lens is when focused at infinity. Some imagine that is the definition of focal length, but it is merely one setting for it. Zoom lenses also vary focal length.

When focused closer than infinity, the lens is extended forward (the frontal elements are, or possibly only internal elements) so that the internal focus node in the lens is further from the sensor plane. If we instead assume focal length is the distance from this internal node to the sensor plane, then of course the focal length is a bit longer when focused closer. That longer focal length changes things, like f-number, which can affect exposure, so regular lenses don't allow distances shorter than some nominal close distance, typically at around 0.1x magnification.

• I certainly did not say the focal length of the lens is also the flange distance. Please read again :) Oct 29, 2018 at 6:10
• @YuvalWeissler Maybe English is not your primary language? When you say, "... the distance from the lens to the image plane (which we can equate with the flange distance)... " that ("... the focal length of the lens is also the flange distance") is exactly what you are saying Oct 29, 2018 at 6:50

Lenses are characterized by their optical and physical properties. Field of view is not an optical property, but a consequence of the camera system to which the lens is attached. The same 50mm lens has different fields of view when paired with differently sized sensors, such as crop frame vs full frame.

Unlike the angle of coverage, the field of view, or angle of view are not lens properties. They depend on the focal length of the lens, the size of the sensor and the distance between the rear focal point and the sensor. When a lens is focused at infinity, the distance between the rear focal point and the sensor is zero. When the lens is focused on something closer, the sensor is placed behind the focal point. The location can be determined with the thin lens formula:

1/F = 1/S1 + 1/S2, Where F is the focal length of the lens, ans S1 and S2 are the subject and image distance respectively.
https://en.wikipedia.org/wiki/Angle_of_view

In the link above it can be seen that the angle of view depends on S2. If S1 is large, F and S2 are approximately the same, and one can say that the field of view is related to the focal length. In macro photography the subject distance S2 is not very large, therefore it has a significant influence, and the field of view is no longer related to the focal length of the lens. Because we are used to relating the field of view to the focal length, we define the effective focal length f, as the image distance. In that case the field of view is related to the effective focal length, which depends on the subject distance.

• This is not hard. Focal length is to where the lens focuses behind. The focal length marked on the lens is when focused at infinity. When focused at a closer distance, the lens elements must be moved forward to still focus on the same image plane. That can be several possible longer focal lengths (over a small range), so the one at infinity is simply the one marked. Any lens formula must use the actual focal length for the actual focused distance. If at 1:1 magnification, the focal length behind is the same as the focused distance in front. Or focused at infinity is half that behind then. Oct 28, 2018 at 19:12
• @Orbit We're talking about photographic lenses here, which are, excepting some novelty acts, complex lenses, not simple lenses, let alone an idealized thin lens. Oct 28, 2018 at 20:11
• @Orbit ~ cameras use complex lenses, not thin lenses. While this can still be calculated the result is the projected image of the lens, which is not what the camera 'sees'. What the camera 'sees' depends on the sensor size, which is why APS-C has a crop factor. The effective field of view is not a purely optical phenomenon. Oct 29, 2018 at 2:17
• When the spacing between various elements of a compound lens is changed, the focal length of the combined system can and very often will also change. Each time any element of the compound system is moved in relation to the other(s), the properties of an equivalent thin lens are also changed. This is just as true when focusing elements move inside a prime lens with independently moving elements/groups as it is when zooming a varifocal lens. Oct 29, 2018 at 2:20
• @Orbit When you use an extension tube, you usually lose infinity focus which is the conventional way of expressing focal length. You are increasing the distance between the lens and the imaging plane in exchange for a much closer focus distance. Oct 29, 2018 at 7:40