Physics - Geometrical Optics Question with Solution | TestHub

Given: Separation of lens for two of its position, $d=10\mathrm{cm}$ Ratio of size of the images in two positions $$\frac{I_1}{I_2}=\frac{3}{2}$$ Distance of object from the screen, $D=$ ? Applying formula, $$\begin{array}{rl}& \frac{I_1}{I_2}=\frac{(D+d{)}^2}{(D-d{)}^2}\\ & \Rightarrow \frac{3}{2}=\frac{(D+10{)}^2}{(D-10{)}^2}\\ & \Rightarrow \frac{3}{2}=\frac{D^2+100+20D}{D^2+100-20D}\\ & \Rightarrow 3D^2+300-60D=2D^2+200+40D\\ & \Rightarrow D^2-100D+100=0\end{array}$$ On solving, we get $D=99\mathrm{cm}$ Hence the distance between the screen and the object is $99\mathrm{cm}$.