Two thin convex lenses of focal length f1 and f2 are separated by a horizontal distance d  (where d < f1 and d < f2) and their centres are displaced by a vertical separation $∆$as shown. Taking the origin of coordinates O at the centre of first lens, x and y coordinates of the focal point of this lens system, for a parallel beam of rays coming from the left, are given by:
    

Image I1 from first lens will act as virtual object for second lens. For second lens – 

$u=(f_1-d);f=+f_2$
$\frac{1}{v}=\frac{1}{f}+\frac{1}{u}=\frac{1}{f_2}+\frac{1}{(f_1-d)}$  
  
  $v=\frac{f_2(f_1-d)}{f_2+f_1-d}$
x-coordinate  $=d+\frac{f_2(f_1-d)}{f_2+f_1-d}=\frac{f_1{f}_2+d(f_1-d)}{f_1+f_2-d}$
Linear magnification,   $m=\frac{v}{u}=\frac{f_2}{f_1+f_2-d}$
The second image will be formed at   $m\Delta$
So, y-coordinate  $=\Delta -m\Delta$
         $=\Delta (1-\frac{f_2}{f_1+f_2-d})$                    
                             
         $=\frac{(f_1-d)\Delta }{(f_1+f_2-d)}$