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I was looking at the Leitz Hektor and Ken Rockwell says

"This is a conventional long lens design, not a telephoto. Its diaphragm sits right at 135mm from the image plane.

The Nikkor lens shown above is a telephoto design, and is much shorter."

https://kenrockwell.com/leica/135mm-f45.htm

But I am not certain of what the difference is

I noticed that some old Russian lenses are very long too, above 80mm

I read in Why is there no apparent relation between focal length and physical lens size? that "Telephoto lenses are by definition lenses which are shorter than their focal-length."

I deduct that there are probably more elements, or magnifying lenses to allow telephoto lenses to be shorter

Otherwise, what is the difference ? are there advantages to long lenses, such as fewer elements?

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The advantage of a non-tele long lens is exactly as you say: fewer elements. I have a 400 mm M42 lens that has only three elements: the achromat doublet at the end of the tube, and the simple meniscus behind the aperture. A 400 "tele" would be much shorter, but it would have additional elements to change the effective focal length of a much shorter-focus objective set. For instance, there might be a four-element Tessar type, with independent focal length as short as about 200 mm, with aperture in the middle, and a three-element achromatic negative group near the mounting flange, to make a "400 mm" telephoto that's only about 240 mm from film/sensor to aperture.

Along with fewer air-glass surfaces, simpler lenses are also much less expensive to produce to high quality -- my 400mm triplet has only three pieces of glass, and no glass-to-glass cemented joins, while a tele-Tessar has seven elements, and three glass-to-glass cement joints (assuming the focal extender elements are a cemented triplet, as is often the case with quality ones).

The other side of this is that "simpler" long lenses are often seen and treated as "bargain" optics, so they don't always receive the level of quality control you might get in a lens that will be offered at a higher price (perhaps because it's shorter and easier to handle). And even though lighter in actual weight (due to much less glass), they may feel heavier because all the glass is as far from the camera body as it can get.

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A telephoto lens has an additional lens/lens group with a negative focus after the primary positive focus objective lens/lens group. The negative focus group expands the image circle created by the objective group, which increases the size of the image circle, thereby reducing the recorded FOV and increasing the effective FL... that negative focus group is called the telephoto group.

It is exactly the same thing as a TC/tele-converter, which is added to a normal lens... only the telephoto group is incorporated as an integral part of the lens design as opposed to being a somewhat mismatched add-on.

IDT you could say there are clear advantages to either design. The more you bend the light, and pass it through additional lens elements, the more likely there will be artifacts/optical errors. But almost all modern long FL designs are telephoto, and the improvements in modern design/materials/manufacture mostly outweigh any simplicity advantage.

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Focal length is a measurement taken from a cardinal point called the rear nodal to the image plane when the camera is focused on a far distant object such as a star. On an optical bench an artificial star is substituted.

The “normal” lens for any camera is applied to a lens with a focal length that is approximately equal to the diagonal measure of the film or digital sensor. A telephoto lens is generally considered to be lens with a focal length that is twice “normal” or greater.

When constructing a long lens to image sporting events, wildlife, or the like, it is probable that such as lash-up will be massive and thus unwieldy. Lens makers can mitigate by intentionally shifting the rear nodal forward. Keep in mind, camera lenses, to thwart aberrations, consist of numerous individual glass elements. Some are air-spaced, some are cemented together, and some are dense glass, some lighter materials, some with positive power, some negative power. Deploying this type of construction allows the optician great latitude as to the location of the rear nodal.

A true telephoto is a long lens with the rear nodal shifted forward. It can even fall forward of the front lens. This design significantly shortens the barrel length as compared to long lens of the same focal length.

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