Question

1)if the image is n times smaller than the object then what will be the object distance for concave mirror in terms of focal length
2)if the image is n times larger than the object then what will be the object distance for convex mirror in terms of focal length

Answer 1

1)   m = - v/u = -1/n
      v =  u n             (u,v,f are negative)
     1/f = 1/u + 1/v
          =  (n+1)/ (n u)
    u = f (n+1)/n 
 Distance  =  | f |  * (n+1)/n

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2)  For a convex mirror the image is smaller than object.  So there are three possible cases:

   a)  concave mirror and image is n times larger.  Real image.
           m = - v/ u = - n
           v = n u
      1/f = 1/ v + 1/ u = (n+1) / ( u n)
       distance = | u | = (n+1) / n *  | f | 

   b)  concave mirror and image is n times larger. virtual image
         m = - v/u = n
         v = - u n
        1/f =  1/u - 1/un 
             =  (n-1)/ ( un )
       distance = | u | = f (n-1) / n

  c)  The mirror is convex and image is smaller n times.
         m = - v/u = 1/n
         v = - u/n

         1/f = 1/u + 1/v 
              = (1 - n) / u
         distance = | u | = (n-1) f