An object and a concave mirror of focal length f=10cm both move along the principal axis of the mirror with constant speeds. The object moves with speed V0=15cms−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=30cm, the speed of the mirror Vm 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 Vm is _______ cms−1

Question

An object and a concave mirror of focal length f=10cm both move along the principal axis of the mirror with constant speeds. The object moves with speed V0=15cms−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=30cm, the speed of the mirror Vm 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 Vm is _______ cms−1

Infinity Learn · Accepted Answer

As shown in figure below, we consider mirror velocity to be on the right side
Question Image

Using mirror formula, position of image is obtained as

u = - 30 c m f = - 10 c m \Rightarrow v = \frac{f_{0}}{u - f} = - 15 c m

Magnification of object is given as

m = \frac{1}{2}

Relative velocity of image with respect to mirror is given as

V_{I M} = m^{2} V_{O M} = \frac{1}{4} V_{O M}

As image is at instantaneous rest, we use

V_{1} = 0

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