Past exam of the physics 2 paper of the University of Oxford / 2013 resit / 4 / Solution

Assume a converging thin lens with $f>0$, a real object, and a real image on the detector. For positive object and image distances $u,v$, the thin lens equation gives $uv=f(u+v)$. Put $S=u+v$. ThenSince $S>0$, $S\ge 4f$, with equality at $u=v=2f$. ThereforeBelow this separation no real conjugate pair exists for one ideal thin lens; a diverging lens alone cannot form a real image of a real object on the detector.