Decrease FF lens focal length for use on APS-C and still have it focus?

Question

Need to convert very cheap vintage FF 50mm f/2.8 lens to work as 35mm lens for for APS-C, for having wider angle of view.

Its kind of works by simply placing lens closer to camera sensor (without adapter) however focus does not work.

I assume it can be made to focus if i change distance between lens elements?

What elements i need to space out to restore focus ability, can correct spacing be figured out mathematically?

I am not a tech savvy please explain in great details using plain language if possible.

Lens has total 4 elements, two closer to the image plane are glues together

Answer 1

This is exactly what a telecompressor/focal reducer/"speed booster" is for. It can be bought as a ready made unit with a choice of mirrorless camera mounts on one side and a choice of SLR/DSLR mounts on the other. Since these devices are more expensive than normal adapters, it can be worth buying strategically in case you have multiple legacy mounts in use (eg buy a telecompressor that accepts Canon EF mount lenses, since simple and inexpensive adapters for a lot of other camera mounts exist for EF mount).

Answer 2

Lens designs, even in the olden days, are highly optimized for sharpness and several kinds of optical aberrations. Even small changes, including distance between elements, are bound to degrade image quality. So, usually, you don't want to tamper with the existing design.

Instead you add lenses, either in front (fish eye lens) or between lens and camera (focal reducer, tele converter).

EDIT:

For some of those Russian lenses, there are hacks to adapt them to Nikon F. E.g. you can add a distance ring before the innermost lens group of a Helios 44 to make it focus to infinity, even with a thin adapter. But the image is not as sharp as before.

You can also find instructions for adaptions without changing the lens geometry, e.g. https://www.youtube.com/watch?v=MPQ8H0BECDQ

The focal length will remain 50mm, with a crop factor of 1.5 that's like 75mm on FF.

Answer 3

The block diagram for your lens appears to be a variation of the Zeiss Tessar design created by Dr. Ralph Rudolph.

Roger Cicala, in one of his excellent blog entries at lensrentals.com says:

Literally dozens of today’s excellent lenses are simply modifications of the Tessar: Leitz Elmars, Zeiss Sonnars, Kodak Ektars, Schneider Xenars, Voigltander Heliostigmats and Skopars, even the Nikon 50mm f/1.8 are all Tessar variations. If you own (a) lens in the 35 to 110mm range providing very good quality at a reasonable price, usually with maximum apertures of f/2.8, chances are it’s a fairly direct descendant of the Tessar.

These lenses typically use what is known as unit focusing. That is, the entire unit, including all elements and the aperture diaphragm all move as one unit when focusing. If you change the spacing of the various groups, your image will only get blurrier. To change the size of the image circle projected by the lens, you would need to change the shape of the rear optical elements.

Answer 4

The only way to get your lens to focus to infinity, is to move the lens further from the film/sensor plane, to where it was designed to be.

I assume it can be made to focus if i change distance between lens elements?

What elements i need to space out to restore focus ability, can correct spacing be figured out mathematically?

What is the basis of your assumption? Understand that most of what determines focal length is the shapes of the individual lens elements (that is, the curvatures of the front and back surfaces). If you re-grind the lenses precisely, you could conceivably hack this lens to work for you. I know of nobody who has done this, or would do it. I don't think any camera repair shop would re-grind lenses.