An object is kept at rest on the principal axis of a lens. Initially the object is at a distance...

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An object is kept at rest on the principal axis of a lens. Initially the object is at a distance three times the focal length f of the lens. The lens runs towards the object at a constant speed \( u \), until the distance between the object and its real image becomes \( 4 f \). If the image always forms on a moving screen then express the velocity of the screen as a function of time.
(a)
\[
v_{i}=u+\left[1-\left\{\frac{f^{2}}{(u t+4 f)^{2}}\right\}\right]
\]
(b)
(c)
(d) None of these
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