We see ourselves in the mirror every morning. How does a mirror work? Figure 18.2 shows light originating from a point and striking a mirror. That point is labeled O and we call it the object; this is where the object really is and where the light originates. Each ray is reflected according to the law of reflection, that the angle of reflection (r) equals the angle of incidence (i); this is indicated for one ray but it is true for every ray. After reflecting from the mirror, these rays diverge as if they had originated from the single point behind the mirror that is labeled I. This is the image. In this case it is called a virtual image; the light does not pass through the image but only appears to be coming from it. A plane mirror produces a virtual image behind the mirror. Dotted lines in the figure are extensions of the outgoing rays; they show where the rays look as though they had come from. Our eyes see light that looks like it came from this point; that is what we mean by the image.

But we can be more specific. Figure 18.3 shows just two rays from the many rays of Figure 18.2. Ray OP leaves the object normal to the mirror, strikes the mirror, and is reflected back upon itself. It could have come from anywhere along the line IP. Ray OQ leaves the object and strikes the mirror at point Q where it is reflected according to the law of reflection. After leaving the mirror it looks like it originated somewhere along line IQ. Of course point I is the only place consistent with both these rays. Q is any point at all so I is the image; the light looks like it came from point I. In Figure 18.3 there are two identical right triangles. Angles OPQ and IPQ are both right angles. Angle f is the same for both. And length PQ is certainly the same for both. Therefore side OP equals side IP. These have also been labeled d_o for object distance and d_i for image distance. Thus, the virtual image produced by a plane mirror is just as far behind the mirror as the object is in front of the mirror. This is true for every point on the object and image. That means the image will be exactly the same size as the object (we could say it has a magnification of 1.00). The image is also right-side-up or erect. The image in a mirror undergoes a right-left reversal; when you wave at your image with your right hand the wave is returned by the left hand of your image.

It is fun to look at the images produced by multiple reflections. Figure 18.4 shows two mirrors set perpendicular to each other. An object is placed at point O. Image I₁ is produced by a single reflection from mirror #1 and image I₂ is produced by a single reflection from mirror #2. But there is still another image, I₁₂ produced by two reflections, from both mirror #1 and #2. You can think of this as the image in mirror #2 of image I₁ or the image in mirror #1 of image I₂. Each reflection reverses the image from right to left. So image I₁₂ is not reversed at all. Wave at yourself in such a corner mirror and see which hand waves back! Or hold up your Adventures in Physics book in front of such a corner mirror and read its title!

Q: How many images are produced by two mirrors placed at 60 to each other?

A: Symmetry is an important aspect of Physics. Symmetry will often allow an easy solution to an otherwise difficult problem. Instead of looking at all the individual rays and their reflections, we will apply symmetry to this problem.

Object O is place between Mirror #1 and Mirror #2. Rays that undergo a single reflection on Mirror #1 produce image I₁; a single reflection from Mirror #2, image I₂. Mirror #1 produces an image of Mirror #2; this is labeled M₁₂. There is an image in that mirror, I₁₂. That image is the result of two reflections--from Mirror #1 and then Mirror #2. Likewise, image I₂₁ is also the result of two reflections from Mirror #2 and then Mirror #1. Three reflections are also possible and produce one more image, labeled I₁₂₁ or I₂₁₂. This is the principle of a Kaleidoscope. Each point on the object appears as five images for a total of six things to look at!