Question

(i)A pin of length 2 cm is placed perpendicular to the principal axis of a converging lens. An inverted image of size 1 cm is formed at a distance of 40 cm from the pin then focal length of lens and its distance from pin are what
please explain the question with proper explanations

Answer 1

h =  2 cm        h' = 1 cm
image is inverted =>  image is real.
     m = - v/u = h'/h = -1/2
          u = - 2 v
     u is negative and v is positive

     -u + v = 40 cm
         3 v = 40  cm          =>  v = 40/3 cm
             u = - 80/3 cm

   1/f = 1/v - 1/u =  3/40 + 3/80 = 9/80

       f  = 80/9 cm

Answer 2

h =  2 cm        h' = 1 cm
     m = - v/u = h'/h = -1/2
          u = - 2 v
  
-u + v = 40 cm
2v + v = 40 cm
         3 v = 40  cm         
            v = 40/3 cm
             u = - 80/3 cm

   1/f = 1/v - 1/u =  3/40 + 3/80 = 9/80

       f  = 80/9 cm