An object and a concave mirror of focal length f = 10 cm both move along the principal axis of the mirror with constant speeds. The object moves with speed V₀= 15 cms^-1 towards the mirror with respect to a laboratory frame. The distance between the object and the mirror at a given moment is denoted by u. When u = 30 cm, the speed of the mirror V_m is such that the image is instantaneously at rest with respect to the laboratory frame, and the object forms a real image. The magnitude of V_m is ____cms^-1.

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Detailed Solution

We can solve by using
$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$
Magnification $m = - \frac{1}{2}$
$V_{0} m^{2} + V_{i} = (1 + m^{2}) V_{m}$
Given that $V_{i} = 0$
$\begin{array}{l} \Rightarrow 15 \frac{1}{4} + 0 = (1 + \frac{1}{4}) \cdot V_{m} \\ V_{m} = 3 cm / s \end{array}$