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Show that when light reflects from two mirrors that meet

Chapter 25, Problem 2

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QUESTION:

Show that when light reflects from two mirrors that meet each other at a right angle, the outgoing ray is parallel to the incoming ray, as illustrated in the following figure.

                

Figure 25.51 A corner reflector sends the reflected ray back in a direction parallel to the incident ray, independent of incoming direction.

Questions & Answers

QUESTION:

Show that when light reflects from two mirrors that meet each other at a right angle, the outgoing ray is parallel to the incoming ray, as illustrated in the following figure.

                

Figure 25.51 A corner reflector sends the reflected ray back in a direction parallel to the incident ray, independent of incoming direction.

ANSWER:

Solution  2PE

Assume the incident ray reflects at an angle ∅ with the first mirror. Since both mirror meet each other at a right angle, so the first reflection ray forms a right triangle with the two mirrors as shown in below figure:

o - ∅

Now from the figure, the angle between the line parallel to the first mirror and outgoing ray is ∅2 and,

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