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(D) The distance between the object (bulb on one wall) and the image (on the opposite wall) is given as $d = 3\;m$.For a convex lens to form a real im

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$0.75$

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(D) The distance between the object (bulb on one wall) and the image (on the opposite wall) is given as $d = 3\;m$.For a convex lens to form a real image of an object on a screen at a fixed distance $d$,the condition for the existence of the image is $d \ge 4f$,where $f$ is the focal length of the lens.To find the maximum possible focal length,we set $d = 4f$.Therefore,$f_{\max} = \frac{d}{4}$.Substituting the given value: $f_{\max} = \frac{3}{4} = 0.75\;m$.Thus,the maximum possible focal length of the lens required is $0.75\;m$.

The image of a small electric bulb fixed on the wall of a room is to be obtained on the opposite wall $3\;m$ away by means of a large convex lens. What is the maximum possible focal length (in $m$) of the lens required for the purpose?

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