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
4Lu
B
3Lu
C
6Lu
D
9Lu

Solution

## The correct option is C $$\displaystyle\frac{6L}{u}$$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,$$AO'=\dfrac{L}{2}+2(\dfrac{L}{2})$$$$=\dfrac{3L}{2}$$Similarly $$BO'=\dfrac{3L}{2}+2(\dfrac{3L}{2})$$$$=\dfrac{9L}{2}$$Hence AB=$$\dfrac{9L}{2}-\dfrac{3L}{2}=3L$$Time taken to cover this distance=$$\dfrac{3L}{u}$$Similarly time taken to cover CD=$$\dfrac{3L}{u}$$Thus total time he is visible is $$\dfrac{6L}{u}$$Physics

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