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(D) For a real object and a real image formed by a convex lens,the minimum distance between the object and its real image is $4f$,where $f$ is the foc

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$x + x' \geq 2f$

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(D) For a real object and a real image formed by a convex lens,the minimum distance between the object and its real image is $4f$,where $f$ is the focal length of the lens.Let $u$ be the object distance and $v$ be the image distance from the optical center.According to the figure,the object distance is $|u| = x + f$ and the image distance is $|v| = x' + f$.The total distance between the object and the image is $D = |u| + |v| = (x + f) + (x' + f) = x + x' + 2f$.Since the minimum distance between a real object and its real image is $4f$,we have $D \geq 4f$.Substituting the expression for $D$,we get $x + x' + 2f \geq 4f$.Therefore,$x + x' \geq 2f$.

An object is placed at a distance $x$ from the focus of a convex lens,and its image is formed at a distance $x'$ from the other focus,as shown in the figure. Which relation do the distances $x$ and $x'$ satisfy?

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