Discussion
What is the minimum distance between an object and its real image formed by a convex lens?
Answer: A
The minimum distance is 4f.
With object distance \(u\) and image distance \(v\), the total separation is \(D = u+v\), and the lens formula gives \[\frac{1}{v} - \frac{1}{-u} = \frac{1}{f} \Rightarrow \frac{1}{u} + \frac{1}{v} = \frac{1}{f}\]
Minimising \(u+v\) subject to that condition gives \(u = v = 2f\), so \[D_{min} = 2f + 2f = 4f\]
Below this separation a convex lens cannot form a real image at all.
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