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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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$\frac{d}{4}$
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 $\frac{d}{4}$
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 $\frac{d}{4}$
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