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Two large plane mirrors $M_{1}$ and $M_{2}$ are kept at an angle of $120^{0}$ as shown in figure. The coordinates of intersection of plane mirror is (0, 2 meter). A man moves along
x-axis. Find the length $l$ (in meter) on x-axis for which man can see image of point A formed by mirrors. (Height of man is negligible). If $l$ is $4 \sqrt{x}$ , find x = ?

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answer is 3.

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Detailed Solution

$\tan 60^{0} = \frac{x}{2} x = 2 \sqrt{3} m$

Hence total length $= 4 \sqrt{3} m$

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