Have you ever wondered how it is possible for the beam of car
headlights reflected from the rear reflector of a bike is returned to the eyes of the driver no
matter where the car is in relation to the bike?
If the reflector was simply a flat mirror then the beam would only reflect into their eyes for one position of the car – in fact you would only see the bike if it was directly in front of you (a)! If the bike was to one side the reflection would not meet their eyes and the bike and rider would effectively disappear (b). (Figure 1)
However real bike reflectors are not plane. They are made of a large number of small tetrahedrons set together so that there are dips in between in the shape of a corner of a right angled cube. This is difficult to draw in 3D so we will look at the 2D version where a beam of light hits the corner of a square (Figure 2).
You should see from the two diagrams in Figure 2 that whatever angle the light beam hits the corners it will reflect back along its original path.
The same is true in 3D for the bicycle reflector. This means that it does not matter where the car headlights are – if any light hits the reflector it will be reflected back towards the car and the cyclist will be seen no matter where they are (Figure 1(c)).