Lens Design for Special Purposes

Hi everybody and glad to be here and seeing all of you.
I am a physics graduated person with no experience in experiments related to lens and photography and I have a question about a relatively simple lens design but due to lack of time I have not been able to do extensive research on this issue and am badly confused.

My question is that I have a lens at hand(3 lens system with two plano-convex and one concave lens in between) that projects film on screen(wall) located nearly 2 m away from it and I want to modify it and make the project as close as half meter with enough magnification.

What should I do and where should I go to get required knowledge?

I have read the ultimate guide for classic lens design and am not confident if it suffice.

Any thought or hint will be greatly appreciated.

Thanks in advance

You are essentially setting up a projector for a closer screen. Think overhead projector, slide projector, etc.

You just need to readjust distance of your lens from the source (commonly called refocusing) to project a focused image at the shorter distance. The projected image will be scaled down geometrically.

If you wanted to maintain the same size projected image at 0.5m as you have at 2m, then you will want to acquire a shorter focal length lens, shorter as the ratio of the two distances, i.e. 4x shorter focal length.

P.S. No need to design optics from scratch... projectors and projector lenses are readily available on ebay. ;)

Thanks a lot Nodda Duma, it was simpler than what I thought.

Can't I simply make lens following tutorials on YT to construct one from scratch? I have access to all the tools that normally are required for this purpose.

Just for learning and mastering. I totally agree though that there are lots of things to experiment with on ebay (and I have some lenses and old projectors too).