Question

a divergent lens has afocal length of 30cm at what distance should an object of height 5sm 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

Hi,

Focal length of divergent lens, F = −30 cm
Distance of image from the lens, v = −15 cm
Using lens formula
$$\begin{gathered} \frac{1}{F}=\frac{1}{v}-\frac{1}{u} \\ \Rightarrow \frac{1}{-30}=\frac{1}{-15}-\frac{1}{u} \\ \Rightarrow \frac{1}{u}=\frac{1}{-15}+\frac{1}{30}=\frac{-2+1}{30} \\ \Rightarrow u=-30\mathrm{cm} \end{gathered}$$

Thus, object is at a distance of 30 cm from the lens.

Magnification(m) is given by
$$\begin{gathered} m=\frac{v}{u}=\frac{{\mathrm{h}}_{\mathrm{image}}}{{\mathrm{h}}_{\mathrm{object}}} \\ \Rightarrow \frac{-15}{-30}=\frac{{\mathrm{h}}_{\mathrm{image}}}{5} \\ \Rightarrow {\mathrm{h}}_{\mathrm{image}}=\frac{5}{2}=2.5\mathrm{cm} \end{gathered}$$
Thus, the height of the image is 2.5 cm.