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

The distance between the object and the real image formed by a convex

1.	The distance between the object and the real image formed by a convex lens is d. IF the linear magnificationis m, find the focal length of the lens in terms of d and m.
Answer» Solution :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) wehave `d=((1+m)f)/m+f(1+m)` which gives `f=(MD)/(1+m)^2`