Question

a convex lens of focal length f produces a real image x times the size of an object then the distance of the distance of the object from the lens is

Answer 1

Dear student,
$$\begin{gathered} u=distanceofobject \\ v=distanceofimage \\ Also(v/u)=x \\ (1/v)–(1/u)=(1/f) \\ \therefore 1–(v/u)=(v/f) \\ \therefore 1–x=(v/f)\therefore v=f(1–x)forrealimagexisnegative \\ \therefore v=f(1+x) \\ asu=(v/x) \\ henceu=[f(1+x)/x \end{gathered}$$

regards