?Corner Reflectors Suppose the three coordinate planes are all mirrored, forming a

Chapter 11, Problem 52

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Corner Reflectors Suppose the three coordinate planes are all mirrored, forming a corner reflector, and a light ray given by the vector  first strikes the -plane, as shown in the figure. Use the fact that the angle of incidence equals the angle of reflection to show that the direction of the reflected ray is given by  Deduce that, after being reflected by all three mutually perpendicular mirrors,the resulting ray is parallel to the initial ray. (Scientists have used this principle, together with laser beams and an array of corner reflectors on the moon, to calculate very precisely the distance from Earth to the moon.)