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Question

# Two plane mirrors are arranged parallel to one another each moving with a speed u as shown in figure. The linear velocity of the Nth image formed by mirror, of a point object (w.r.t object), considering the first reflection takes place at mirror 1 is :

A
Nu
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B
4Nu
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C
3Nu
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D
2Nu
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Solution

## The correct option is D 2Nu With respect to mirror-I, the object is going away from mirror. So, first image will also move away w.r.t. mirror-I with speed u. So with respect to object ′O′, the image speed is vimage1, obj=vimage1, mirror1 + vmirror1, obj vimage1, obj=u+u=2u Now, this image acts as object for mirror-II. With respect to mirror-II, the image is going away towards left with speed 3u. So, the second image formed by mirror-II will move away towards right with speed 3u w.r.t. mirror-II . Hence, speed of 2nd image formed by mirror w.r.t. ′O′ will be 3u+u=4u Generalizing this for Nth image formed by mirror, we can say, vimage N, obj=2Nu Why this question? To understand the image velocity when an object is placed between two parallel mirrors.

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