Question

15. Show that incident ray CA || DB
reflected ray if two mirrors are kept
perpendicularly as shown in the give
figure.

Answer 1

Answer:

angle BOA=90°(given)

anglePBO=90°(normal ray is always perpendicular)

anglePAO=90°

since we know that in a quadrilateral sum of all angles is 360°

hence angleBPA=90°

Now in triangle PBA

angle2 + angle3 = 90° —(1)

now by laws of reflection

angle1=angle2—(2)

and,angle3 = angle 4—(3)

from 1,2 and 3

angle 1 + angle 4 =90°—(4)

on adding 1 and 4 we get

angle 1 +angle2+angle3+angle4=180°

so angleBAC + angle ABD = 180°

hence CA is parallel to DB since sum of cointerior angles is 180°.

prooved