Question

At what distance from a concave mirror of focal length 10 cm should an object 2 cm long be placed to get an erect image 6 cm tall?

Answer 1

Given that focal length, f= -10cm

Magnification, m= Image height/ Object height= 6/2 = 3

Also magnification= - v/u

3= -v/u

v= -3u

As 1/u + 1/v = 1/f

1/u + 1/-3u = 1/ -10

Therefore u= -6.667

So object should be placed at a distance of 6.667 cm in front of the mirror.

Answer 2

concave mirror , f is negative ,  f = -10 cm
   u = ?
 h = 2 cm 
 erect image  so  h' is positive,  h' = 6 cm
     so m = h'/h = 3
         as  m = -v/u = 3  => v = -3 u

   mirror equation  is  1/v + 1/u = 1/f

       1/(-3u) + 1/u = 1/(-10)
          2/(3u) = -1/10
            u = -20 /3 cm = -6.67 cm         and  v = -3 u = 20 cm
           v is positive,  so image is behind the mirror and is virtual.

  in concave mirror , an erect image is obtained when the object is between the pole and the focus. it is magnified and is virtual.  so  you can verify from values of u, v and f.