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?

Question

vikas askiitian expert · Answer

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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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?

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?

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