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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 :

131657_06f4e568ff45427187cf7006e6af931c.png


A
4Lu
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B
3Lu
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C
6Lu
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D
9Lu
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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 $$\dfrac{6L}{u}$$

577208_131657_ans_3567b4b30a14409986ca78c9bc6812f9.png

Physics

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