question_answer

At what distance from a convex lens of focal length 30 cm, an object should be placed, so that the size of the image be \[\frac{1}{2}th\] of the object?

A)  \[30\,cm\]      

B)  \[60\,cm\]

C)  \[15\,cm\]      

D)  \[90\,cm\]

Correct Answer: D

Solution :

The image formation by a convex lens is as follows: Image formed is diminished, when object lies between 2F and infinity. Magnification \[(M)=\frac{image\,size}{object\,size}\] \[=\frac{1}{2}=\frac{v}{u}\] ?.(i) From lens formula, \[\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\] ?.(ii) where / is focal length, v the image distance and u the object distance. From Eqs. (i) and (ii), we get \[\frac{1}{f}=\frac{1}{u}+\frac{2}{u}\] Given,       \[u=90\text{ }cm\] \[\therefore \] \[\frac{1}{30}=\frac{3}{u}\] \[\Rightarrow \] s\[u=90cm\]