In Fig. 6.33, 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. Prove that AB || CD.

Question

Philoid · Accepted Answer

It is given in the question that:

PQ is parallel RS

And,

BE parallel to CF

According to laws of reflection, we know that:

Angle of incidence = Angle of reflection

∠1 = ∠2 and,

∠3 = ∠4 (i)

The diagram is given below:

And,

∠2 = ∠3 (Alternate interior angles, since BE, is parallel to CF and a transversal line BC cuts them at B and C respectively) (ii)

From (i) and (ii), we get

∠1 + ∠2 = ∠3 + ∠4

⇒ ∠ABC = ∠DCB

⇒ AB parallel CD (Alternate interior angles)