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 $N^{th}$ image formed by mirror, of a point object (w.r.t object), considering the first reflection takes place at mirror $1$ is :

Answer 1

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 ${}^{\prime }{\text{O}}^{\prime }$, the image speed is

$v_{\text{image1, obj}}=v_{\text{image1, mirror1}}+v_{\text{mirror1, obj}}$

$v_{\text{image1, obj}}=u+u=2u$

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. ${}^{\prime }{\text{O}}^{\prime }$ will be $3u+u=4u$

Generalizing this for $N^{th}$ image formed by mirror, we can say, $v_{\text{image N, obj}}=2Nu$

Why this question? To understand the image velocity when an object is placed between two parallel mirrors.