Question

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

• A. $+1.3$
• B. $-1.3$
• C. $+1.8$
• D. $-1.8$

Answer 1

The correct option is B $-1.3$

From the figure,

$u=-(25+f)$

$v=(40+f)$

Using lens formula we get

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

$\frac{1}{f+40}+\frac{1}{25+f}=\frac{1}{f}$

$65f+2f=1000+65f+f^2$

$f^2=1000$

$f=31.623cm$

$\therefore u=25+31.62=56.62cm$

$v=40+31.623=71.62cm$

$m=\frac{v}{u}=\frac{71.62}{-56.62}=-1.3$