(Solved) : Two Flat Rectangular Mirrors Both Perpendiculars . . .

Two flat rectangular mirrors, both perpendiculars to a horizontal sheet of paper, are set edge to edge with their reflecting surfaces perpendicular to each other.
(a) A light ray in the plane of the paper strikes one of the mirrors at an arbitrary angle of incidence θ 1. Prove that the final direction of the ray, after reflection from both mirrors, is opposite to its initial direction. In a clothing store, such a pair of mirrors shows you an image of yourself as others see you, with no apparent right–left reversal.
(b) What If? Now assume that the paper is replaced with a third flat mirror, touching edges with the other two and perpendicular to both. The set of three mirrors is called a corner-cube reflector. A ray of light is incident from any direction within the octant of space bounded by the reflecting surfaces. Argue that the ray will reflect once from each mirror and that its final direction will be opposite to its original direction. The Apollo 11 astronauts placed a panel of corner cube retro reflectors on the Moon. Analysis of timing data taken with it reveals that the radius of the Moon’s orbit is increasing at the rate of 3.8 cm/yr as it loses kinetic energy because of tidal friction.

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