Relation between Object and Image velocity for a spherical mirror along principal axis.

 

We know the mirror formula is:

Case 1: differentiating the above equation w.r.t. time, we get

the (-ve) sign shows that if the direction of object is in positive direction, then the direction of image will be in opposite direction i.e. object and image will always have their velocities opposite to each other. In other words, if the object approaches the mirror then the image will go away from the mirror and vice versa.

In case |u| = |v|

i.e. |m| = 1

This will be observed when the object is at the center of curvature.

Case 2: When object moves between center of curvature and focus:

In this case for a concave mirror the image will lie beyond C.

So, |v| > |u|

Speed of image will be more than the speed of the object.

Case 3: Object moves between focus & pole of the mirror

In this case, for a concave mirror the image will lie behind the mirror.

The image is also virtual and

u is (-ve)

f is (-ve)

v is (+ve)

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