Question

A divergent lens has a focal length of $30$cm. At what distance should an object of height $5$cm from the optical centre of the lens be placed so that its image is formed $15$cm away from the lens? Find the size of the image also.

Answer 1

We know that for a divergent lens both u and f are -ive , from lens equation

$v=\frac{uf}{u+f}$ , as both u and f are -ive therefore v will be -ive ,

given $f=-30cm,v=-15cm$ ,

so $u=\frac{fv}{f-v}=\frac{-30\times -15}{-30-(-15)}=-30cm$ ,

now linear magnification $m=I/O=v/u$ ,

given height of object $O=5cm,I=?$ ,

therefore $I/5=15/30$ ,

or $I=5\times 15/30=2.5cm$