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 both 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 \[(M)=\frac{image\,size}{object\text{ }size}\]                   \[=\frac{1}{2}=\frac{v}{u}\]                         ??? (i) From lens formula,                 \[\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\]                      ???.. (ii) where \[f\]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,       \[u=90\text{ }cm\] \[\therefore \]  \[\frac{1}{30}=\frac{3}{u}\] \[\Rightarrow \]               \[u=90\text{ }cm\]