An object is approaching towards a convex mirror from a long distance. Will the image move with the same velocity as the object? In which direction will be image move?

Explanation

In case of spherical mirror,
`(1)/(v) + (1)/(u) = (1)/(f)`
Differentiating with respect to t we get,
`-(1)/(v^(2))(dv)/(dt) - (1)/(u^(2))(du)/(dt) = 0 or, (dv)/(dt) = - (v^(2))/(u^(2))(du)/(dt)`
Here, `(dv)/(dt)` = velocity of image, `(du)/(dt)` = velocity of object Clearly, the velocity of the image
`= - (v^(2))/(u^(2)) xx "velocity of the object"`
`= - ((v)/(u))^(2) xx "velocity of the object"`
In case of convex mirror, `m = |v|/|u| lt 1`
So, the velocity of the image `lt` valocity of the object. The negative sign of equation (1) indicates that the image is moving towards the mirror. So, the image will move towards the mirror with less velocity than the object.