Problem 2PE

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.

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,

∅2 = 90o -

Substitute 90o - for in the above expression,

∅2 = 90o - ( 90o - ∅ )

= ∅

So, the outgoing ray makes an angle ∅ with a line parallel to the first mirror.

Therefore by the properties of parallel lines the outgoing ray is parallel to the incident ray.

Hence the outgoing ray is parallel to the incident ray.