derive lens maker formula by concave lens

Lens maker's Formula: It is a relation that connects the focal length of  a lens to radii of curvature of the two surfaces of the lens and the refractive index of the material of the lens. following assumption are considered while deriving lens maker's formula for concave lens
a) only point object is taken
b) the aperature of the lens is small
c) the lens is thin

the image formation can be seen in terms of two steps:
a) the first refracting surface fors the image of the object. 
b) the image acts as a virtual object for formation of final image I by the second surface
According to the equation
$$\begin{gathered} \frac{{\mathrm{n}}_1}{\mathrm{OB}}+\frac{{\mathrm{n}}_2}{{\mathrm{BI}}_1}=\frac{{\mathrm{n}}_2-{\mathrm{n}}_1}{{\mathrm{BC}}_1}----\left(\mathrm{i}\right) \\ -\frac{{\mathrm{n}}_2}{{\mathrm{DI}}_1}+\frac{{\mathrm{n}}_2}{\mathrm{DI}}=\frac{{\mathrm{n}}_2-{\mathrm{n}}_1}{{\mathrm{DC}}_2}----\left(\mathrm{ii}\right) \\ \mathrm{for} \mathrm{the} \mathrm{thins} \mathrm{lens} {\mathrm{BI}}_1={\mathrm{DI}}_1 \mathrm{adding} \left(\mathrm{i}\right) \mathrm{and} \left(\mathrm{ii}\right) \\ \mathrm{we} \mathrm{get} \\ \frac{{\mathrm{n}}_1}{\mathrm{OB}}+\frac{{\mathrm{n}}_1}{\mathrm{DI}}=\frac{({\mathrm{n}}_2-{\mathrm{n}}_1)}{{\mathrm{BC}}_1+{\mathrm{DC}}_2} \\ \mathrm{By} \mathrm{the} \mathrm{sign} \mathrm{convention} {\mathrm{BC}}_1=-{\mathrm{R}}_1, {\mathrm{DC}}_2 =+{\mathrm{R}}_2 \\ {\mathrm{n}}_1\mathrm{f}=\frac{({\mathrm{n}}_2-{\mathrm{n}}_1)}{-{\mathrm{R}}_1+{\mathrm{R}}_2} \\ -\mathrm{f}=\frac{\left({\displaystyle \frac{{\mathrm{n}}_2}{{\mathrm{n}}_1}}-1\right)}{{\mathrm{R}}_1-{\mathrm{R}}_2} \end{gathered}$$