A luminous object is separated from a screen by distance $d$. A convex lens is placed between the object and the screen such that it forms a distinct image on the screen. The maximum possible focal length of this convex lens is

Focal length of a convex lens by displacement method Focal length of the convex lens $$ f=\frac{a^{2}-b^{2}}{4 a} $$ where $a$ = distance between the image and object and $b=$ distance between two positions of lens Fact The distance bemeen the ho points should be 4 times greater than the focal iength of the convex lens, ie, $d>4 f$. So, the maximum possible focal length of this convex lens is $\frac{d}{4}$