A convex lens makes a real image $4cm$ long on a screen. When the lens is shifted to a new position without disturbing object or the screen, we again get a real image on the screen which is $9cm$ long. The length of the object must be :

The correct option is B $6cm$
Given: A convex lens makes a real image 4 cm long on a screen. When the lens is shifted to a new position without disturbing object or the screen, we again get a real image on the screen which is 9 cm long.

To find the length of the object

Solution:

Let the height of the object be $h_1$

At the first position,

$m_1=\frac{4}{h_1}=-\frac{v}{u}$

At the second position,

$m_2=\frac{9}{h_1}=-\frac{u}{v}$

Now, $m=m_1\times m_2⟹(-\frac{v}{u})\times (-\frac{u}{v})=\frac{4}{h_1}\times \frac{9}{h_1}⟹h_1^2=36⟹h_1=6cm$

Hence the length of the object should be 6 cm.