question_answer

An object and its real image are located at distances 25 cm and 40 cm respectively from the two principal foci of a convex lens. The linear magnification of the image is near to

A)  + 1.3                    

B)  - 1.3

C)  + 1.8                    

D)  -1.8

Correct Answer: B

Solution :

                In the figure                                 \[u=-(25+f)\]                                 \[v=(40+f)\] using     \[\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\]                 \[\frac{1}{f+40}=\frac{1}{25+f}=\frac{1}{f}\]                 \[65f+2f=1000+65\,f+{{f}^{2}}\]                 \[{{f}^{2}}=1000\]                 \[f=31.62\,cm\]                 \[u=25+31.62\]                 \[=56.62\,cm\]                 \[v=40+31.62=71.62\,cm\]                 \[m=\frac{v}{u}=\frac{71.62}{-56.62}=-1.3\]