The distance between the object and the real image formed by a convex lens is d. IF the linear magnification is m, find the focal length of the lens in terms of d and m.

Explanation

The convex lens formula for a real image is
`1/v+1/u=1/f`
Where no sign conventions are to be used, Multiplying by u we get
`u/v+1=u/f or 1/m=u/f-1=(u-f)/f`
or `m(u-f)=f or u=((l+m)f)/m`……..(ii)
Multiplying (i) by v we get
`1+v/u=v/f or 1+m=v/f or v=f(1+m)`......(iii)
Now u+v=d Using (ii) and (iii) we have
`d=((1+m)f)/m+f(1+m)` which gives `f=(md)/(1+m)^2`