Question

A convex lens placed at a distance of 16 cm from
an object produces an image of magnification
m(ml> 1). If the object is moved towards the lens
by 8 cm, then again an image of magnification m is
obtained. The numerical value of the focal length of
the lens is​

Answer 1

Explanation:

Given A convex lens placed at a distance of 16 cm from  an object produces an image of magnification  m(ml> 1). If the object is moved towards the lens  by 8 cm, then again an image of magnification m is  obtained. The numerical value of the focal length of  the lens is

We know that 1/v – 1/u = 1/f

                So u/v – 1 = 1/f

            Now m = v/u = f / f + u

          Given u1 = - 16, u2 = - 8  

            Also m1 = m, m2 = - m

          Now f/f – 16 = - f / f – 8

        So f^2 – 8 f = - f^2 + 16 f

        2f^2 – 24 f = 0

     So f^2 – 12 f = 0

       Or f = 12 cm