Question

in the given figure, m and n are two plane mirrors perpendicular to each other. show that the incident ray CA is parallel to the reflected ray BD​

Answer 1

Let the normal at A and B meet at P

since angle of incidence = angle of reflection

we have,

$\angle1= \angle2 and \angle4= \angle3$

As the mirrors are perpendicular to each other,

we have

BP || OA and AP|| OB.

$Since BP \perp PA$

we have ,

$\angle APB=90°$

$.:. \angle2+ \angle3=90°$

$; \angle1+ \angle4= \angle2+ \angle3=90°$

So,

$\angle1+ \angle2+ \angle3+ \angle4=180°$

$;: \angle CAB+ \angle ABD=180°$

$Hence, AC||BD$

Answer 2

incident ray CA is parallel to the reflected ray BD