Question

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

Answer 1

F = -30 cm

Height of object = 5 cm

V = 15 cm

$\bf\huge\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$

$\bf\huge\frac{1}{-30}=\frac{1}{15} - \frac{1}{u}$

$\bf\huge\frac{1}{u} = \frac{1}{15} + \frac{1}{30}$

$\frac{1}{u} = \frac{2+1}{30}$

= $\bf\huge\frac{3}{30}$

=> U = 10 cm

Magnification = $\bf\huge\frac{-V}{U}$

$\bf\huge\frac{-15}{10} = \frac{hi}{5}$

hi = -7.5

$\bf\huge\boxed{\boxed{\:Image\:=\:Virtual,\:Enlarged,\:Erect}}}$