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Question

In fig, m and n are two plane mirrors perpendicular to each other. Prove that the incident ray CA is parallel to reflected ray BD.
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Solution

Given: Two plane mirrors m and n, perpendicular to each other. CA is incident ray and BD is reflected ray.
To Prove: CADB
Construction: OA and OB are perpendiculars to m and n respectively.

Proof:

mn,OAm and OBn

AOB=90o
(Lines perpendicular to two perpendicular lines are also perpendicular.)

In ΔAOB,

AOB+OAB+OBA=180o

90o+2+3=180o2+3=90o

2(2+3)=180o (Multiplying both sides by 2)

2(2)+2(3)=180o

CAB+ABD=180o

(Angle of incidence = Angle of reflection)

1=2 and 3=4)

CABD (CAB & ABD form a pair of consecutive interior angles and are supplementary)

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