Question

An object and its real image are located at distances $25\text{cm}$ and $40\text{cm}$ respectively from the two principal focii of a convex lens on either side. The linear magnification of the image is nearly equal to

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

Answer 1

The correct option is B $-1.3$


Here,
$x_1=25\text{cm},x_2=40\text{cm}$
According to Newton's formula
$f^2=x_1{x}_2=\left(25\right)\left(40\right)$
$f=\sqrt{\left(25\right)\left(40\right)}=10\sqrt{10}\text{cm}=32\text{cm}$
Object distance, $u=-(f+x_1)=-(32+25)\text{cm}=-57\text{cm}$
Image distance, $v=(f+x_2)=(32+40)\text{cm}=72\text{cm}$
Magnification, $m=\frac{v}{u}=\frac{72}{-57}=-1.3$