Question

A 2 cm high object is placed at a distance of 32 cm from a concave mirror. The image is real, inverted and 3 cm in size. Find the focal length of the mirror and the position where the image is formed?

Answer 1

concave mirror:
   u = -32 cm       h = 2 cm   h' = -3 cm  image
   m = h'/h = -3/2 
   m = -v/u = -3/2     => v = 3 u /2 = - 48 cm

1/f = 1/ u + 1/v
     = -1/48 - 1/32 = - 5/96
  f = - 19.2 cm

Answer 2

Given :-

u = - 32 cm

h = 2 cm

h' = - 3 cm

To Find :-

f = ?

Solution:-

m = - v/u = h'/h = - 3/2

- v/u = - 1.5

v = - 48

1/f = 1/v + 1/u

1/-48 + 1/-32 = 1/f

= - 5/96

f = - 19.2 cm