Further Reading

Flat mirrors

Two basic principles of the ray model are these:

  • In a uniform medium — air, glass, water — light travels in straight lines.
  • Our brain registers the images from the two eyes against each other, matching points by context. The brain then identifies the distance of a point on an object by tracing back rays and assuming the point is at the convergence point of the traced back rays.

Together with the reflection and refraction principles that tell when light does NOT travel in a straight line, this leads us to think about situations that we can construct where we can bend light to usefully fool the brain. The simplest example of this is the flat mirror. Let's see where the two principles above plus the reflection principle lead. (These are nice examples of a basic tool for building scientific knowledge: "Playing the implications game".)

  • Reflection: When a light ray hits a smooth polished surface (mirror) it bounces off not at random but in a regular way. The incoming angle with the normal (perpendicular) to the surface is equal to the outgoing angle with the normal; or briefly, at a mirror the angle of incidence ($θ_i$) equals the angle of reflection ($θ_r$).

If we have an object and place it in front of a mirror, the light that scatters off the object will spray out in all directions. If the mirror is properly placed, some of those rays will hit the mirror and scatter off according to the reflection principle. What will a pair of eyes interpret if they look at those scattered rays? Two of the rays from the object are shown in the figure below.

What we can see, is that if the brain behind the eyes assumes that the rays it is receiving have come directly from the object — without a bounce — it will assume those rays come along the dotted line extension that is shown continuing behind the mirror. Looking at the geometry carefully and using similar triangles, the result is:

When an object is viewed in a mirror, the viewer's brain interprets it as being behind the mirror by the same distance (as measured along the perpendicular to the mirror) that the object is in front of it.

The rays seen by the eye do not actually meet at a point, but the brain, only knowing the direction of the ray, assumes it came directly form an object. When the rays seen by the eye do not meet, but the brain assumes they do, the image is called virtual. If a screen is put at the position of the virtual image, there are no rays there so nothing will be seen on the screen.

For some this is a really strange result. After all, the light is actually coming from the surface of the mirror. Why doesn't the image appear to be on the mirror? The reason, of course, is that you brain makes assumptions you can't control. You may know that the light is bouncing off the mirror, but the part of your brain that interprets light into images doesn't.

This leads to some challenging and interesting results. As you go through some of the examples and problems, you will come to appreciate the phrase "it's all done with mirrors"!

Workout: Flat mirrors


Joe Redish 4/10/12


Article 708
Last Modified: July 2, 2019