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In the figure given below, let PQ and RS are two mirrors placed parallel to each other. An incident ray AB strikes the mirror PQ at B, the reflected ray moves along the path BC and strikes the mirror RS at C and again reflects back along CD.
What is the relation between AB and CD?

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A B = C D

A B | | C D

A B ⊥ C D

None of these

answer is B.

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Detailed Solution

Given data,
PQ and RS are two parallel mirrors and the incident ray AB strikes the mirror PQ at B.
Drawing the rays

In figure, PQ and RS are two mirrors placed parallel to each other. An incident ray AB strikes the mirror PQ at B, the reflected ray moves along the path BC and

Since

is a transversal, therefore using the alternate interior angles property,

∠ L B C = ∠ M C B ... 1

We know that,
Angle of incidence = angle of reflection

⇒ ∠ A B L = ∠ L B C

and

∠ M C B = ∠ M C D

⇒ ∠ A B L = ∠ M C B ∵ ∠ L B C = ∠ M C B

⇒ ∠ A B L = ∠ M C D .... (2) ∵ ∠ M C B = ∠ M C D

Adding equations (1) and (2), we get,

∠ L B C + ∠ A B L = ∠ M C B + ∠ M C D

⇒ ∠ A B C = ∠ B C D .... (2)

Here, a pair of alternate interior angles

∠ A B C and ∠ B C D

are equal.

∴ A B ∥ C D

Hence, option (2) is correct.

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