In Fig., m and n are two plane mirrors perpendicular to each other. Sh

1.	In Fig., m and n are two plane mirrors perpendicular to each other. Show that incident ray CA is parallel to reflected ray BD.
Answer» Let normals at A and B meet at P. As mirrors are perpendicular to each other, therefore, BP \|\| OA and AP \|\| OB. So, BP ⊥ PA, i.e., ∠ BPA = 90° Therefore, ∠ 3 + ∠ 2 = 90° (Angle sum property) (1) Also, ∠1 = ∠2 and ∠4 = ∠3 (Angle of incidence = Angle of reflection) Therefore, ∠1 + ∠4 = 90° [From (1)] (2) Adding (1) and (2), we have ∠1 + ∠2 + ∠3 + ∠4 = 180° i.e., ∠CAB + ∠DBA = 180° Hence, CA \|\| BD

In Fig., m and n are two plane mirrors perpendicular to each other. Show that incident ray CA is parallel to reflected ray BD.

Answer»

Let normals at A and B meet at P.

As mirrors are perpendicular to each other, therefore, BP || OA and AP || OB.

So, BP ⊥ PA, i.e., ∠ BPA = 90°

Therefore, ∠ 3 + ∠ 2 = 90° (Angle sum property) (1)

Also, ∠1 = ∠2 and ∠4 = ∠3 (Angle of incidence = Angle of reflection)

Therefore, ∠1 + ∠4 = 90° [From (1)] (2) Adding (1) and (2), we have

∠1 + ∠2 + ∠3 + ∠4 = 180°

i.e., ∠CAB + ∠DBA = 180°

Hence, CA || BD