In the given 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 ​

Question

In the given figure PQ and RS are two mirrors placed parallel to each other. An incident ray \(\overline{AB}\) strikes the mirror PQ at B, the reflected ray moves along the path \(\overline{BC}\) and strikes the mirror RS at C and again reflected back along CD. Prove that AB // CD. 

[Hint : Perpendiculars drawn to parallel lines are also parallel]

Answer 1

Draw the normals at B and C. 

then ∠x = ∠y (angle of incidence angle of reflection are equal)

∠y = ∠w (alternate interior angles) 

∠w = ∠z (angles of reflection and incidence) 

∴ x + y = y + z (these are alternate interior angles to \(\overline{AB}, \overline {CD}\)

Hence AB // CD.