What is the derivation of lens formula for convex lens

ΔABC is similar to ΔA’B’C

Therefore, \(frac{AB}{A’B’}=frac{CB}{CB’}\) (equ.1)

Draw DC = AB

In ΔDCF~ ΔA’B’F

\(frac{DC}{A’B’}=frac{CF}{B’F}\) \(frac{AB}{A’B’}=frac{CF}{B’F}\) (equ.2)

From equ.1 and equ.2,

\(frac{CB}{CB’}=frac{CF}{CB’+CF}\) \(frac{+u}{+v}=frac{f}{-v+f}\)

u(-f-v) = fv

Uf – uv = fv

Dividing by u,v,f we get,

\(frac{1}{v}-frac{1}{f}=frac{1}{u}\) \(frac{1}{f}=frac{1}{v}-frac{1}{u}\)

Therefore, above is the derivation of the lens formula for a convex lens.