Question

a divergent lens has a focal length of 20 cm . At what distance should an object of height 4cm from the optical center of the lens be placed so that its image is formed 10cm away from the lens.find the size of the image also

Answer 1

Hi,

Given,
Focal length of divergent lens, f = −20 cm
Distance of image, v = −10 cm
Using lens formula
$$\begin{gathered} \frac{1}{f}=\frac{1}{v}-\frac{1}{u} \\ \Rightarrow \frac{1}{u}=\frac{1}{v}-\frac{1}{f} \\ \Rightarrow \frac{1}{u}=\frac{1}{-10}-\frac{1}{-20} \\ \Rightarrow \frac{1}{u}=\frac{-20+10}{200}=\frac{-10}{200} \\ \Rightarrow u=-20\mathrm{cm} \end{gathered}$$
So, the object is at a distance of 20 cm from the lens(left side).

$$\begin{gathered} \mathrm{Magnification}\left(m\right)\mathrm{is}\mathrm{given}\mathrm{by} \\ m=\frac{v}{u}=\frac{{\mathrm{h}}_{\mathrm{image}}}{{\mathrm{h}}_{\mathrm{object}}} \\ \Rightarrow \frac{-10}{-20}=\frac{{\mathrm{h}}_{\mathrm{image}}}{4} \\ \Rightarrow {\mathrm{h}}_{\mathrm{image}}=\frac{1}{2}\times 4=2\mathrm{cm} \end{gathered}$$