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The are three plane mirrors of which opposite two are parallel and adjacent ones are mutually perpendicular such that they would have made three sides of a cuboid. A ray starts from point A and hits the mirror 1, mirror 2 and mirror 3 in succession respectively and reaches A again. The distance of point A from mirror 1, mirror and mirror 3 are a, b, and c respectively. Match the statement in list I with the results in list II.

LIST I LIST II
A Angle of incidence at mirror 1 P a rectangle
B Angle of incidence at mirror 2 Q a parallelogram
C Angle of incidence at mirror 3 R $\cot^{- 1} \frac{a + c}{b}$
D The quadilateral formed first ray and three reflected rays will form S $\tan^{- 1} \frac{a + c}{b}$
T $\tan^{- 1} \frac{2 a + 2 c}{b}$

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$A - R, B - S, C - R, D - Q$

$A - P, B - Q, C - R, D - T$

$A - R, B - S, C - P, D - R$

$A - P, B - Q, C - R, D - S$

answer is A.

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Detailed Solution

Take an incident beam From A on mirror 1, The reflected beam will appear to come from image of A (A’). A’ will act as object for mirror 2 and the reflected beam will come from image of A’ (B) by mirror2. B will act as object for mirror 3 and the reflected beam will appear to come from image of B (C) formed by mirror 3. The final ray will be CA. Complete all the rays from this diagram

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