What type of lens do I need to build a ciné film scanner

I want to build a scanner to digitise standard 8mm ciné film using my Eumig 8mm projector and a Raspberry Pi with the High Quality camera module. I am not too worried about the mechanical, electronics and programming side of things, but I am not sure what type of lens to use.

I have a 50mm, f/2, C-mount lens from my Zorki-4K 35mm camera, and I intend to try that before looking for a specific lens for the camera module (which has a C-mount and a CS adapter).

A standard 8mm frame has a diagonal of 5.6mm, and the RPi HQ camera’s sensor has a diagonal of 7.9mm, so 1:1 magnification would be ideal. Will my 50mm lens be suitable, and how do I calculate the object distance and sensor distance from the lens (and from what point on the lens axis)? If my 50mm is not suitable, what type of lens should I look for?

I will, of course, be replacing the projector’s incandescent lamp with a white LED for the purposes of scanning.

Hopefully, I have included enough information.