In a 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 moves along the path BC and strikes the mirror RS at C and again reflects back along CD. Prove that AB is parallel to CD

In a 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 moves along the path BC and strikes the mirror RS at C and again reflects back along CD. Prove that AB is parallel to CD

Answer:

AB is incident ray to mirror PQ. Let it make an angle of incidence i1 with the normal at the point of contact B. The angle of reflection is r1. By law of reflection i1 = r1. BC reflected ray becomes incident ray for mirror RS and it makes angle of incidence i2 and angle of reflection r2 which are equal i2 = r2

Since normals are drawn to parallel mirrors, the two normal are parallel to each other

So r1 = i2 but i1 = r1 = i2 = r2

Since i1 + r1 = i2 + r2 (alternate angles) for the rays AB and CD and BC is transversal.

So AB is parallel to CD. AB || CD
 

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Updated on: 10-Oct-2022

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