obtain the formula for the focal length of a lens in terms of object distance and magnification.

We know,

For a lens, 1/f = 1/v – 1/u

And, magnification, m = v/u

=> v = mu

So, 1/f = 1/mu – 1/u

=> 1/f = (1/u)(1/m – 1)

=> 1/f = (1/u)(1 – m)/m

=> f = mu/(1 – m)