In figure 5.37 PQ and RS are two mirrors which are parallel to each other. An incident ray AB getting reflected from point B of the mirror PQ and moving along the path BC again gets reflected from point C of the mirror RS and moves along the path CD. Then prove that AB || CD.

Given:

PQ || RS

Theory:

⇒ If a transverse intersecting 2 lines and alternate angles forms are thus equal then 2 lines are parallel

In reflection

∠ incidence =∠ reflection

∠ ABC = ∠ i + ∠ r = 2∠ i

∠ BCD = ∠ i + ∠ r = 2∠ i’

Draw perpendicular from both point B and C

The perpendicular from point B and C are parallel to each other

If BC act as transverse between both perpendicular lines

Alternate angles will be equal

That is

⇒ ∠ i = ∠ i’

Then ∠ ABC = ∠ BCD alternate angles

And 2 straight lines AB and CD having transverse BC

∴ AB || CD