Question

Two plane mirrors of length $L$ are separated by distance $L$ and a man $M_2$ is standing at distance $L$ from the connecting line of mirrors as shown in figure. A man $M_1$ is walking in a straight line at distance $2L$ parallel to mirrors at speed $u$, then man $M_2$ at O will be able to see image of $M_1$ for time :

• A. $\frac{4L}{u}$
• B. $\frac{3L}{u}$
• C. $\frac{6L}{u}$
• D. $\frac{9L}{u}$

Answer 1

The correct option is C $\frac{6L}{u}$

The light from man $M_1$ hits the mirror and then reaches the man $M_2$. The positions of the moving man needs to be found when the light from him hits the corners of the mirror to reach the standing man.

From geometry,

$A{O}^{\prime }=\frac{L}{2}+2\left(\frac{L}{2}\right)$

$=\frac{3L}{2}$

Similarly $B{O}^{\prime }=\frac{3L}{2}+2\left(\frac{3L}{2}\right)$

$=\frac{9L}{2}$

Hence AB=$\frac{9L}{2}-\frac{3L}{2}=3L$

Time taken to cover this distance=$\frac{3L}{u}$

Similarly time taken to cover CD=$\frac{3L}{u}$

Thus total time he is visible is $\frac{6L}{u}$