JEE Advance - Physics (2022 - Paper 2 Online - No. 8)
An object and a concave mirror of focal length $f=10 \mathrm{~cm}$ both move along the principal axis of the mirror with constant speeds. The object moves with speed $V_{0}=15 \mathrm{~cm} \mathrm{~s}^{-1}$ 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 $u=30 \mathrm{~cm}$, 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 _________ $\mathrm{cm} \,\mathrm{s}^{-1}$.
Answer
3
Explanation
Magnification,
$$ \begin{aligned} & m =\frac{f}{u-f} \\\\ & =\frac{10}{30-10}=\frac{1}{2} \end{aligned} $$
Also $\quad m^2=\frac{v_m}{v_0-v_m}$ [where, $v_m=$ speed of mirror]
$$ \begin{aligned} & m^2\left(v_{\mathrm{o}}-v_{\mathrm{m}}\right) =v_m \\\\ & \Rightarrow \left(v_0-v_m\right) \times \frac{1}{4} =v_{\mathrm{m}} \\\\ & \Rightarrow v_0 =5 v_m \\\\ & \Rightarrow v_m =\frac{v_0}{5}=\frac{15}{5} \\\\ & \Rightarrow v_m =3 \mathrm{~cm} / \mathrm{s} \end{aligned} $$
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