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If an object far away from convex mirror moves towards the mirror, the image also moves. Does it moves faster, slower or at the same speed as compared to the object?
let a object is placed at distance from convex mirror of focal length f....
applying mirror formula
1/v+1/u=1/f...................1
differentiating eq 1 wrt to time
dv/dt (-1/v^2) -du/dt(1/u^2)=0..........2
velocity of image =dv/dt=Vi
velocity of object=du/dt=Uo
from eq 2
Vi=Vo(-v^2/u^2) (-v/u=m(magnification))
Vi=-m^2Vo...............3
now here are two cases when magnification is equal to 1 and <1
if at any instant particle is at 2f then its image will have same speed but other than this position image will be slower than object speed because m<1 for other positions....
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