How am I supposed to prove that the image produced on a paper (reflected of a concave mirror) is in focus?

It is not quite clear what you are asking for. "What is the relation between the position of the object, the position of the image and the focal length? " The object is a distance do from the mirror.

The image is a distance di from the mirror. The focal length is f The relationship is: 1/f = 1/do + 1/di See link http://www.physicsclassroom.com/class/re... Is that what you mean?

This is basically what I wanted thanks for your help appreciate it ( im not that good in physics not my best subject).

I cant really gove you an answer,but what I can give you is a way to a solution, that is you have to find the anglde that you relate to or peaks your interest. A good paper is one that people get drawn into because it reaches them ln some way.As for me WW11 to me, I think of the holocaust and the effect it had on the survivors, their families and those who stood by and did nothing until it was too late.