Actual focal length determination WRT distance focused

By definition "focal length" is figured at infinity. For purposes of figuring angle of view you might want to factor in the lens extension. With most lenses you could simply measure the distance the lens moves forward as it focusses closer, and add that to the marked focal length. True telephotos often consist of a positive front component which moves forward while the negative rear stays in place. I'm not sure if this method would work there.

More important at close(st) focusing distance is the parallax compensation.

I would guess that if a lens is measured at 51 - 52 mm focused to infinity and about 55mm when focusing closely then the difference is going to be very small. Are you really intending to fill the frame this tightly?

My query is more academic than practical, but it woud be nice to know.

The apparent focal length at a given magnification is 1+M. At 1:1 it's 2x, and at 1:2 it's 1.5x. At infinity M->0, so the apparent focal length will approach 1x. The real focal length of a lens is always measured at infinity and is by definition the distance from the optical center of the lens at which something like the sun forms a single point. The easiest way to determine it is to photograph an object of a known size at a known distance to calculate the magnification, then work out the focal length from the distance and mag. If the object is, say 10m and is 10mm on film, then the magnification is M=10mm/10m or 1:1000. The apparent focal length is M*d, the real focal length is M*d/(1+M). So if the 10m object rendered 10mm at 20m you'd have an apparent focal length of 20mm. Real focal length is 19.98mm and you probably couldn't measure accurately enough to tell the difference.

A 35mm lens at 0.7m has a magnification of 1:20. This magnification represents exactly a 5% (1/20) difference in apparent vs real focal length.

The marked focal length of my 1st version rigid Summicron is 51.8mm. In focusing down to one meter the total excursion is approximately 2.5mm which would give a focal length at one meter of 54.3mm. The same principles would apply to lenses of other focal lengths. Teles would add and WAs would subtract.

I just do not get it, the misuse - in my eyes - of the term "focal length".

Just to make certain, can anyone please tell me what the focal length of an otherwise 50mm lens is, once it sits on a 25mm extension ring.

By what i read here the lens now has a focal length of 75mm. Right?

And with a few more extension rings I could make it become a 300mm lens, right? And if I shorten the mount on a lathe, it could well become a 45mm lens, right?

Hogwash, I am afraid, has been passed around here.

There may be a slight variation in focal length with lenses that focus internally, retrofocus and such that move the groups/elements individually when focusing rather tahn the whole lens back and forth, but a 50mm lens is essentially a 50mm lens, give or take a mm or 2.

Focal length does not change by extension, just -maybe- a very tiny bit when internally the lens configuration is changed.

Yes, I suggest you go buy a lux 50 ASPH and shave off 10mm. Then you'll be the only one with a lux 40 ASPH.

Perhaps the confusion is due to sloppy semantics. Each lens has a distinct 'focal length' which is the distance from it optical center to the point where the rays from a light source, an infinite distance away, come to focus. Picture starting a fire with a magnifying glass. The sun at an infinite (for practical purposes) distance away projects light and heat rays through the glass and where they come to focus the heat is concentrated. Often the focal length of a camera lens is not exactly noted. The actual focal length of most Leica 50mm lenses varies somewhat +/- the target of 51.8mm, many of which are so marked (as described in my previous post). Others may have the focal length scratched on the inner barrel somewhere. In any event, the 'nominal' focal length is not usually the actual focal length of that particular lens. When the lens is not focused at infinity, the distance from the optical center to the film plane is not precisely 'focal length' but more properly 'back focus', and it would be more clearly understood if the proper term were used.