In the situation as shown in the figure, the focal length of the thin plane concave lens is 20 cm. A point object P is at distance of 20 cm from the lens. Find the velocity of image formed by plane mirror at the instant as shown in the figure.

detailed solution

Correct option is D

Image formation due to concave lens,  u=−20cm,f=−20cm ∵1v−1u=1fOr   1v+120=−120 ∴v=−10 cm ∵1v−1u=1fOr    −1v2dvdt+1u2dudt=0Or    dvdt=v2u2dudtOr vx=  component of velocity along optical axis =100400×10cos370=14×8=2cms−1    ∵y'y=mOr    y'=my ∴dy'dt=mdydt+ydmdtHere, y = 0           ( ∵object is on optical axis) ∴dy'dt=vy=vu×10sin37o=−10−20×6=3 cms−1For Plane Mirror, Horizontal component : vI-vM = -vo-vM ⇒vI - 1 = -2-1 ⇒vI = 0Vertical Component : vI-vM = +vo-vM ⇒vI - 0 = +3-0 ⇒vI = +3Hence, vimage=+3j^cms−1