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An object is mounted on a wall. Its image of equal size is to be obtained on a parallel wall with the help of a convex lens placed between these walls. The lens is kept at distance x in front of the second wall. The required focal length of the lens will be:
A
less than $\dfrac{x}{4}$
B
more than $\dfrac{x}{4}$ but less than $\dfrac{x}{2}$
C
$\dfrac{x}{2}$
D
$\dfrac{x}{4}$
Detailed Solution
For an equal-size real image, the object and image distances from the lens are equal ($u=v=x$), corresponding to magnification $-1$ (i.e., object at the centre of curvature, $u=2f$). So $x=2f\Rightarrow f=\dfrac{x}{2}$.