Characteristics of Plane Mirrors

Characteristics of Plane Mirrors
••• Froiland Rivera / EyeEm/EyeEm/GettyImages

How would you respond if asked to describe the characteristics of images formed by plane mirrors? First, you would have to be sure you understand the terminology in play. Is a "plane mirror" something you use to check your appearance during a transcontinental flight, or is it something more mundane?

A ​plane mirror​ is the kind of mirror you're probably most used to using, although if social media are any indication, "selfies" had largely come to replace actual mirrors early in the 21st century. Ideally, a plane mirror consists of a perfectly flat surface with no distortions, and bounces 100 percent of the light that strikes it (incident light) back at a predictable angle.

While no mirror is "perfect," ideal entities in physics are fun to talk about. In the course of learning about plane mirrors, you'll get a taste of the general science of optics, and a sense of one of the many ways your eyes can fool you in the course of doing their job exactly as designed.

Optical Properties of Light

Light, despite being almost everywhere a great deal of the time, is a difficult entity to properly describe, like many things in physics. You can appreciate this by simply looking at the number of ways light is represented not only in science texts but in art. Does light consist or particles, or does it consist of waves? Are the waves pointing in a particular direction?

In any case, light visible to humans can be described as having a wavelength λ between about ​440 and 700 billionths of a meter​ (10–9 m, or nm). Since the speed of light ​c​ is constant at about 3×108 m/s in a vacuum, you can determine the frequency of any light source ​ν​ from its wavelength: ​νλ = c​.

When discussing mirrors, it is convenient to represent light not as wave fronts (as you'd see radiating outward after tossing a large rock into a previously placid lake) but as rays. Also, rays coming from the same source and striking adjacent portions of mirrors can be treated as parallel. With this scheme, it is easy to compute the angles involved in plane mirror problems.

Reflection and Refraction

When light rays strike a physical surface, their path can change in a number of ways. The rays can bounce off of the surface, pass through it, or some combination of both.

When light rays bounce off an object, this is called ​reflection​, and when they pass through it and are bent in the process, this is called ​refraction​. The latter is an action of lenses, whereas the only concern with plane (and other) mirrors is reflection.

The ​law of reflection​ states that ​the angle of incidence of light rays striking a plane mirror is equal to the angle of reflection,​ with both measured with respect to a line perpendicular to the surface of the mirror.

Images Formed By Mirrors and Lenses

When mirrors and lenses "process" the light rays that strike them, they "create" images literally shaped by these factors: the distance between the object and the mirror (or lens center) and the shape of the surface.

Lenses by definition include multiple curved surfaces, while ​convex​ (outward-curving) and ​concave​ (inward-curving) mirrors each contain one; plane mirrors represent the simplest scenario of everything mentioned here.

If the image formed is on the same side as the reflected or refracted light rays, it is a ​real image​. This means that for mirrors, a real image would be on the same side as a person looking into it (for lenses, it would be on the other side since light is refracted rather than reflected in this setting). Images that appear behind a mirror (or in front of a lens) are called ​virtual images​.

How can an image form "behind" a mirror? After all, there might be nothing there but solid concrete for hundreds of miles . . . okay, not miles, but the wall could be very thick. But think for a moment: When you look in a mirror, exactly where does "the person" you see ​appear​ to be looking back at your from?

Plane Mirror Image Problem

As implied by the results of the above-suggested exercise, the image appears to be behind the mirror, but actually isn't. It is thus a virtual image. Exactly where and how is this image "found"?

If you draw a diagram showing these situations from above, you can work out the location of the image in any plane-mirror scenario is using the law of reflection. For example, if an observer is standing 3 m from a mirror at an angle of 45 degrees, her image will be found directly opposite her on the other side of the mirror. But how far?

Use the ​Pythagorean theorem​ to determine this. The 3-meter distance between the observer and the mirror is a right triangle with a hypotenuse of 3 and equal sides ​s​ such that

s^2+s^2=3^2\implies 2s^2=9\implies s=2.12\text{ m}

This is the perpendicular distance between the observer and the mirror, so the image is twice this distance from the observer, or 4.24 m.

Other Properties of Plane Mirrors

In addition to being divided into "real" and "virtual," images can also be ​upright​ or ​inverted.​ Anyone who has ever used the inside of a spoon as a mirror has seen an example of an inverted image. Plane mirrors are said to create upright images, but this is a misleading or at least incomplete description of what is happening, because it applies only to the y-axis, or vertical axis.

If you look into a mirror, the top of your head is behind and above your eyes compared to the mirror, and correspondingly, the eyes of the image are closer and lower in relation to the mirror (and you) than the back of the head of the image. The lines connecting these points, as seen from the side, are the same length, but oriented differently (but symmetrically) in space. Thus the image ​is​ inverted – but along the x-axis!

  • Another reason the "flipping" of images in a horizontal direction by plane mirrors is easy to miss, or at least harder to explain, is more biological than physical: When you look in a mirror, you are seeing a being that in general is bilaterally symmetrical (that is, can be divided into equal right and left halves by a vertical plane). If people were in the habit of turning their heads sideways to look into mirrors, this property of mirrors would probably be more firmly ingrained in the everyday person's mind.

Hinged Plane Mirrors

Among the countless examples of plane mirrors in scientific, industrial and household use are hinged plane mirrors. These represent a good way to demonstrate the straightforward, but often difficult to translate into experience, laws governing plane mirrors from the perspective of geometry.

If you have the chance, try setting up an array of three mirrors (you may not have hinges, but that's no hindrance) oriented at mutual 60-degree angles, which from above would look like a bicycle wheel with three equally spaced spokes. If you have a protractor, a light source and some smaller mirrors, you can make and test predictions about reflections you "make" using basic geometry as outlined above.

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