Zoom and magnification relation

Dear all,

I have a mathematical question regarding relation between zoom factor
and magnification. My digital video camera shows me the current zoom
factor selected. Focal is 3,5-91 mm. I'm looking for mathematic
formulas which give me the zoom factor to be selected so that an
object in the shot will appear halved, double, etc. I premise the
object distance is unknown.
Is there any way?

Thank you.
Juky