An object is located on a wall, its image of equal size is to be obtained on a parallel wall with the help…
An object is located on a wall, its image of equal size is to be obtained on a parallel wall with the help of a convex lens. The lens in placed at a distance ' $\mathrm{d}$ ' in front of the second wall. The required focal length of the lens is
less than $\frac{\mathrm{d}}{4}$
more than $\frac{\mathrm{d}}{4}$ but less than $\frac{\mathrm{d}}{2}$
only $\frac{\mathrm{d}}{4}$
only $\frac{d}{2}$
Solution
Size of the image is equal to the size of the object. Hence image distance will be equal to object distance. Also if object distance $u$ $=2 \mathrm{f}$, Image distance will be $2 \mathrm{f}$.
$\begin{aligned}
& \therefore \mathrm{u}=\mathrm{v}=\mathrm{d}=2 \mathrm{f} \\
& \therefore \mathrm{u}+\mathrm{v}=2 \mathrm{~d}=4 \mathrm{f} \\
& \therefore \mathrm{f}=\frac{\mathrm{d}}{2}
\end{aligned}$