Therefore

The size of the image on the sensor divided by the size of the object equals the distance between the sensor and the lens divided by the distance between the lens and the object.

That is I/O = v/u

But v/u isn't much different from the focal length or "f" (unless the lens is very close to the object) therefore, in these situations we can say that

I/O = f/u

A friend was clearing out his office at work today and came across a copy of the Ilford Manual of Photography (or at least it was a later version of it). Just had a browse through it and it feels as though I'm back in a physics class all over again.