Question

What is the object distance? you will need to use the magnification equation to find a relationship between s and s′. then substitute into the thin lens equation to solve for s.?

Answer 1

 For lens in S I system,1/v - 1 /u = 1/f 

gives 1/v=1/f + 1/u, 

multiply by 'u' on both sides 

u/v =u/f + 1 

u/v = ( u+f ) / f 

inverting, 

v/u = f / (u+f) 

Therefore magnification 'm' = v/u=f / (u+f) 

'm' = f / (u+f) 

Given magnification is 5 / 9 

f / (u+f) = 5 / 9 

object distance 'u'= 4f /5 

Now substitute for focal length f ( focal length of diverging lens is negative)