18.1 Image in a Plane Mirror

How do we see something? Consider a point on an object. Light rays come away from that point, traveling out in straight lines as shown in Figure 18.1. When our eye (and brain) detect these rays of light diverging from a common point, we see that point. We do not intercept a handful of rays and then sit down and do a mathematical calculation to see if these rays have come from a common point. But our eye and brain do the equivalent as they detect these rays optically and neurologically. Whenever we detect rays of light coming from a common location, we see something there.

Figure 18.1 We see a point on an object clearly by the rays of light that come away from that point, traveling in straight lines.

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.

Figure 18.2 A plane mirror produces a virtual image behind the mirror just as far as the object is in front of the mirror (di = do).

Figure 18.A You see a virtual image of yourself in the mirror just as far behind the mirror as you are in front of the mirror.

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 do for object distance and di 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.

Figure 18.3 The virtual image produced by a plane mirror is just as far behind the mirror as the object is in front of the mirror.

Fig 18.B Reflections from the smooth surface of a lake or a reflecting pool behave just as from a mirror.

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!

Figure 18.4 Three images are produced in a corner mirror. Wave at yourself in such a corner mirror and see which hand waves back!

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!

Figure 18.C How many images are there? A Kaleidoscope provides six symmetric things to view (the original object plus five images).