A convex lens is placed between a fixed object and a fixed screen. The distance between the object a

Question

A convex lens is placed between a fixed object and a fixed screen. The distance between the object and screen is 1 m . The real images of the object are formed on the screen for two successive positions separated by a distance of 60 cm . If the heights of images formed in the two positions of the lens are 12 cm and 3 cm , respectively, then the actual height of the object is

Professor PC Thomas Classes · Answer

$
\begin{aligned}
& m_1=\frac{h_1}{h_o}=\frac{v}{u} \
& m_2=\frac{h_2}{h_o}=\frac{u}{v}
\end{aligned}
$
As the positions are conjugate to each, reversibility of light.
$
m_1 	imes m_2=\frac{h_1}{h_o} 	imes \frac{h_2}{h_o}=\frac{v}{u} 	imes \frac{u}{v}
\ \frac{h_1 \cdot h_2}{h_o^2}=1
\
h_o=\sqrt{h_1 \cdot h_2}
$