Question

A 2.0 cm tall object is placed perpendicular to the principal axis of a concave lens of focal length 15 cm. At what distance from the lens, should the object be placed so that it forms an image 10 cm from the lens? Also find the nature and size of the image.

Answer 1

$$\begin{gathered} Thelensformulais \\ \frac{1}{v}-\frac{1}{u}=\frac{1}{f} \\ \frac{1}{10}-\frac{1}{u}=\frac{1}{15} \\ \frac{1}{u}=\frac{1}{10}-\frac{1}{15} \\ u=30cm \\ uandvbotharepositivewhichmeansthattheimageisformedonthesamesideastheobject \\ andincaseoflensesitispossibleonlywheniftheimageformedisvirtual. \\ Therefore,theimageformedis\mathit{v}\mathit{i}\mathit{r}\mathit{t}\mathit{u}\mathit{a}\mathit{l}. \\ also, \\ magnification=m=\frac{v}{u}=\frac{10}{30}=\frac{1}{3}=\frac{Sizeoftheimage}{Sizeoftheobject} \\ Sizeofimage=\frac{Sizeofobject}{3}=\frac{2}{3}=0.67cmandpositivesignofmshowsthattheimageiserect. \end{gathered}$$