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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?

Grade:12

1 Answers

vikas askiitian expert
509 Points
11 years ago

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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