Corner reflector

Corner reflector is amazing in its “incom­pre­hen­sible effi­ciency”: the simplest device — three mutu­ally perpen­dic­ular reflecting planes — has a whole range of appli­ca­tions on Earth and in space, too! A reflector on a bicycle or car consists of a large number of these small corners, and large corner reflec­tors — for radio waves — are installed on water buoys and small yachts. And the reflec­tors on the Soviet Lunokhod-1 and Lunokhod-2 moon­lan­ders, as well as those on the US Apollo programme, are being used in an ongoing exper­i­ment in laser lunar loca­tion exper­i­ment — allowing measure­ment of the ever-changing distance from the Earth to the Moon with great accu­racy.

The idea behind corner reflector is simple: a beam (of light, ...) reflecting off three mutu­ally perpen­dic­ular mirrors goes “back” — parallel to the direc­tion from which it came. If the direc­tion of the initial beam is given by vector with coor­di­nates $(a; b; c)$, then after reflec­tion of the beam from the plane $xOy$ its direc­tional vector will be $(a; b; -c),$ and after consec­u­tive reflec­tions from planes $yOz$ and $zOy$ — $(-a; b; -c)$ and $(-a; -b; -c)$ respec­tively.

Unlike head­lights, a reflector (consisting of a large number of small corner reflec­tors) requires no energy and contains no bulbs. But if it is attached to a bicycle, motor­bike, car, if you turn even a small part of a pedes­trian’s jacket or a road sign surface into a reflector with a special coating, the driver of the car, whose head­lights have illu­mi­nated one of the above-mentioned objects, will imme­di­ately see it because of the light reflec­tion from the reflector.

Large corner reflector is easy to make by cutting mirrors at your local work­shop. It’s also possible to make it your­self out of plastic — there are plas­tics avail­able now that have a good reflec­tion coef­fi­cient. Once you make a big model you can see that reflec­tion in the corner reflector follows you when you move. And if you stand in front of the reflector and close your eyes one by one, you will find that each time the reflec­tion of the open eye looks directly at you and always out of the inter­sec­tion of the mirror planes!

The model with a number of large corners looks spec­tac­ular when mounted under the ceiling in a school corridor.

Math­e­matikum Gießen