The Corner Reflector

When two vertical mirrors are placed at right angles as shown in Figure (1), a horizontal ray approaching the mirrors is reflected back in the direction from which it came. It is a little exercise in trigonometry to see that this is so. Since the angle of incidence equals the angle of reflection at each mirror surface, we see that the angles labeled θ1 must be equal to each other and the same for the angles θ₂ . From the right triangle ABC, we see that θ₁ + θ₂ = 90°. We also see that the angles θ₂ + θ₃ also add up to 90°, thus θ₃ = θ₁, which implies the exiting ray is parallel to the entering one. If you mount three mirrors perpendicular to each other to form the corner of a cube, then light entering this so called corner reflector from any angle goes back in the direction from which it came. The Apollo II astronauts placed the array of corner reflectors shown in Figure (2) on the surface of the moon, so that a laser beam from the earth would be reflected back from a precisely known point on the surface of the moon. By measuring the time it took a laser pulse to be reflected back from the array, the distance to the moon could be measured to an accuracy of centimeters. With the distance to the moon known with such precision, other distances in the solar system could then be determined accurately.

Figure 1: With a corner reflector, the light is reflected back it the same direction from which it arrived.

Figure 2: Array of corner reflectors left on the moon by the Apollo astronauts. A laser pulse from the earth, aimed at the reflectors, returns straight back to the laser. By measuring the time the pulse takes to go to the reflectors and back, the distance to that point on the moon and back can be accurately measured.