Question

A divergent lens has focal length 30cm .At what distance from the optical center should the object of 5 cm be placed so that the image is formed 15 cm aesy from the lens? Also find height of the image.Draw a ray diagram to illustrate the situation.

Answer 1

Hi,

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

Magnification(m) is given by
$$\begin{gathered} m=\frac{v}{u}=\frac{h_{image}}{h_{object}} \\ \Rightarrow \frac{-15}{-30}=\frac{h_{image}}{5} \\ \Rightarrow h_{\mathrm{image}}=2.5\mathrm{cm} \end{gathered}$$