Is focal length internal or external? [duplicate]

Question

I just wanted to check because I've encountered various distinctly different assertions.

I was originally taught that focal length referred to the optimum distance from subject| ←→|lens, where sharpest focus is achieved.

More recently I'd come across information from macro photographers claiming that it's actually subject| ←→|sensor, but dependant on the lens.

Currently I'm reading about geometric optical engineering & the physics of light, reflection, refraction, etc. Material that seems to imply that the subject is not involved; it's simply the distance from the centre of the lens| ←→|sensor (or eye, or wherever the image is being cast).

Answer 1

The camera lens is a converging lens. Light rays entering the lens are caused to bend inward due to the shape of lens and its material of construction. We can trace out the path of these light rays as they travel inside the camera. This trace resembles a cone of light. The distance from lens to the apex of this cone is the focal length. This measurement is taken when the object being imaged is at an infinite distance. The ideal target for this assessment is a star. However, lens makers make this measurement indoors on an optical bench that creates an artificial star using a focused light source.

Now the camera lens suffers from seven major aberrations that combine to degrade the resulting image. To mitigate this, a quality camera lens is a complex array of several lenses of different shapes (powers). Some are convex, some are concave, some are dense glass, some are less dense. Such construction shifts the measuring point. This point is called the rear nodal. It could fall at about the center of the lens barrel or in the air behind or ahead of the lens. Generally it falls somewhere within the lens barrel.

The distance from the rear nodal to the image plane is a variable based of subject distance. It is at its shortest when imaging a distant object. This distance steadily elongates as the target object gets closer the camera. As an example, when doing extreme close-up photography, this distance, now called the “back focus”, can be quite long. If you are working in close, and achieve life-size, the distance from the rear nodal is twice the focal length.

Answer 2

Focal-length is a property of the lens. It has nothing to do with the distance of focus which is called focus distance. A lens of a given focal-length can focus anywhere within its focus-range, usually up to infinity from its minimum focus distance. For example, a Canon EF 35mm F/2.8 IS USM has a 35mm focal-length and can focus from 23cm to infinity, while the Canon EF-S 35mm F/2.8 Macro IS STM is also a 35mm focal-length lens too but can focus from 13cm to infinity.

A lens by its design has a Minimum Focus Distance. This is also a physical property that cannot be changed unless you add loupes at the front or extension tubes at the back (either passive or active) but that minimum focus distance is measured in two ways. When specified for a lens alone such as lenses sold for DSLRs, Mirrorless and Medium Format cameras, it is specified as the distance from the sensor (or film) to the point where an object would be in focus. When specified for a camera with a built-in lens, it is specified from the front of the lens element. This is why Canon has cameras with a minimum focus distance of 0cm (zero) such as the Powershot SX540 HS.

A lens also has a maximum focus distance which is nearly always infinity. Some lenses though such as the Canon MP-E 65mm Macro do not focus to infinity.

The focus distance is therefore simply the distance that the lens is focused at. It is usually only measured as distance from the lens. This is what will be shown on a lens if it has a focus-scale or on a camera's viewfinder, mostly for cameras with EVFs.

Answer 3

There is focused distance in front of the lens, and there is focal length behind the lens. When the lens is focused on infinity in front, then the length behind the lens to the sensor is called focal length. Technically, these are measured from node points usually inside the lens, but wide angle and telephoto are situations putting them outside the lens body.

When the focused distance becomes shorter than infinity, the lens is racked out and the length behind becomes longer (2x at 1:1), however the "marked focal length" number on a lens applies only when focused at infinity. It does change with focus distance.

For a normal rectilinear lens (not fish eyes), the ratio of
distance in front of the lens / distance behind the lens
is the same ratio as
real size of the subject in front / size of subject in image.
This is the reproduction ratio, or the magnification factor.