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# Two plane mirrors A and B are alligned parallel to each other as shown. A ray of light is incident at an angle $30^{\circ}$ at a point just inside on one end of mirror A. What is the maximum number of reflection the ray undergoes before it emerges out.

$(a)\;28 \\ (b)\;30 \\ (c)\;32 \\ (d)\;34$

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## 1 Answer

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In $\Delta CBA$
$\angle A=30^{\circ}$
$\tan 30 =\large\frac{x}{AB}$
$\large\frac{1}{\sqrt 3} =\frac{x}{.2}$
$\therefore x =\large\frac{.2}{\sqrt 3}$
For every distance x a reflection takes place.
$\therefore$ number of reflections $= \large\frac{2 \sqrt 3}{x}$
$\qquad= \large\frac{2 \sqrt 3 \times \sqrt 3 }{0.2}$
$\qquad=30$
Hence b is the correct answer.
answered Jan 20, 2014 by

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