1.

If you run towards a plane mirror at a speed 2m/s at what speed does the apparent distance between you and your image decrease.

Answer»

We know, in case of PLANE mirror ,
|Object distance|= | image distance |
⇒ Xom = - Xim
Here, Xom is object distance with RESPECT to mirror
Xim is image distance with respect to mirror.

now, difference with respect to time ,
⇒dXom/dt = - dXim/dt
⇒Vom = - Vim
If mirror doesn't move Vm = 0
Then, Vo = - Vm
MEANS , if I run towards a plane mirror with speed 2m/sec then, my image also runs towards mirror with speed 2m/sec but in opposite direction.
HENCE, total DECREASES in distance between my position to image position = 2 × 2 = 4m

Hence, answer should be 4 m


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