Question

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Two planes mirrors are placed perpendicular to each other as shown in the figure.An incident ray AB to the first mirror is first reflected in the direction of BC and then reflected by the second mirror in the direction of CD.Prove that AB ll CD.

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Answer 1

Step-by-step explanation:

Given: Two plane mirrors m and n, perpendicular to each other. CA is incident ray and BD is reflected ray.

To Prove: CA∥DB

Construction: OA and OB are perpendiculars to m and n respectively.

Proof:

∵m⊥n,OA⊥m and OB⊥n

∴∠AOB=90

o

(Lines perpendicular to two perpendicular lines are also perpendicular.)

In ΔAOB,

∠AOB+∠OAB+∠OBA=180

o

⇒90

o

+∠2+∠3=180

o

⇒∠2+∠3=90

o

⇒2(∠2+∠3)=180

o

(Multiplying both sides by 2)

⇒2(∠2)+2(∠3)=180

o

⇒∠CAB+∠ABD=180

o

(Angle of incidence = Angle of reflection)

∴∠1=∠2 and ∠3=∠4)

⇒CA∥BD (∠CAB & ∠ABD form a pair of consecutive interior angles and are supplementary)

Answer 2

in the direction of BC and then reflected by the second mirror in the direction of

Step-by-step explanation:

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m shyam

class 12

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