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Question
Show that the least possible distance between an object and its real image in a convex lens is 4f, where f is the focal length of the lens.
Solution
Let d be the least distance between the object and image for a real image formation.
`1/f = 1/v - 1/u`, `1/f = 1/x + 1/(d - x) = d/(x(d - x))`
fd = xd - x2, x2 - dx + fd = 0, x = `(d ± sqrt(d^2 - 4fd))/2`
For real roots of x, d2 - 4fd ≥ 0
d ≥ 4f.
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