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  4. 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

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Q. 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

WBJEEWBJEE 2014Ray Optics and Optical Instruments

Solution:

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 between the two points should be greater than four time the focal length of the convex lens, i.e., $d >4 f$.
So, the maximum possible focal length of this convex lens is $\frac{d}{4}$.