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Question

Two plane mirrors of length L are separated by distance L and a man M2 is standing at distance L from the connecting line of mirrors as shown in figure. A man M1 is walking in a straight line at distance 2L parallel to mirrors at speed u, then man M2 at O will be able to see image of M1 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 6Lu
The light from man M1 hits the mirror and then reaches the man M2. 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=L2+2(L2)

=3L2

Similarly BO=3L2+2(3L2)

=9L2

Hence AB=9L23L2=3L

Time taken to cover this distance=3Lu

Similarly time taken to cover CD=3Lu

Thus total time he is visible is 6Lu

577208_131657_ans_3567b4b30a14409986ca78c9bc6812f9.png

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