The wonders of optics/The laws of reflection.—Mirrors
THE LAWS OF REFLECTION.—MIRRORS.
When a ray of light falls obliquely on any polished
surface, as that of a mirror, a piece of water, a plate
of burnished metal, or any other reflecting substance,
the ray, like an elastic ball, is immediately projected in
a contrary direction to that in which it fell. Moreover,
the direction in which it is reflected is at right angles
to the surface, and in the same plane as that of the ray
in the first instance. This experiment may be tried
very easily, and will show the reason for the two following
laws.
1. The angle of incidence is equal to the angle of reflection, and vice versâ.
2. Reflection can only take place in one direction—in that of the incident rays, both of which are always in a plane perpendicular to the reflecting surface.
The following figure will assist the student in performing experiments on the reflection of light from flat surfaces.
The ray A B falling obliquely on the horizontal mirror, is reflected upwards at the same angle in the direction B C. This may be proved geometrically by placing a graduated circle in a vertical position in the plane A B C, when we shall find that the angle A B D formed by A B (the incident ray) with the perpendicular D B is equal to the angle formed by this perpendicular line and the reflecting ray B C. You may also prove in the same way that these three lines are all in the same vertical plane.
Fig. 13—Reflection from Plane Surfaces.
Let us now examine the effects of light reflected from plane surfaces. We must first, however, notice a certain optical illusion to which we are continually falling a prey, almost without our knowledge. We always fancy objects to be in reality in the place where we see them, and, in spite of our having already enumerated a large number of these deceptions, we must still add one more to the list. In reality we rarely see objects in the place where they really are; for if by the effect of reflection, refraction, or any other cause, the rays of light are made to deviate from their course, we no longer see the object from which they proceed in its real position, but in the direction taken by the luminous pencil at the moment of entering the eye.
For instance, if the ray A B is bent during its passage to the eye at B, and consequently reaches it in the direction B C, it is at A1, and not at A, that we shall see the object from which it proceeds. Every ray of light which passes out of a medium of a certain density into
Fig. 14.—Refraction
another of a different density is bent from its primary course, or, in scientific language, it is refracted. The
Fig. 15.—Experimental Proof of Refraction.
experiments we made in a former chapter on the properties of the prism are founded on this principle. The law may be easily illustrated by allowing a ray of light to fall upon the surface of a vessel of water, as shown in the preceding figure.
The light of the stars and planets undergoes a similar deviation when passing in its course through the earth's atmosphere; and at the moment we see the rising of the sun, the moon, or a star, they are in reality still
Fig. 16.—The Effects of Plane Mirrors.
below the horizon. Our eyes consequently are still deceiving us, no matter what part of the domain of optics we may enter.
There are two kinds of mirrors—plane and curved. We will first examine the properties of the former sort, being those which are ordinarily applied to the usages of every-day life.
In the figure in the preceding page we have a young lady looking at her reflection in a tall cheval glass. Every point upon the surface of her clothes and face is reflected back to her eye from the surface of the tin amalgam which has been applied to the back of the mirror by the looking-glass maker, for the purpose of rendering the image of the object more brilliant than if the glass alone were used. The rays which proceed from every one of these points strike upon the surface of this metallic layer, are stopped by its opacity, and are reflected
Fig. 17.—Reflection from the Surface of Water.
back to the eye at an angle equal to that at which they strike the surface. The image seen by the eye is formed, consequently, by the reflection of every one of these rays; and as we always see objects in the direction taken by the luminous ray at the moment it enters the eye, we fancy we see objects before us that are really behind, or on each side of us. For instance, the ray starting from the left foot of the young lady in the figure is reflected from the point indicated on the surface of the glass, but the eye does not stop here, but sees the foot at an equal distance beyond the mirror.
The same thing takes place, not only with glass, but with all substances having polished surfaces. Still water, which to all intents and purposes has a polished surface, reflects the objects within its range as perfectly as a mirror.
The preceding observations apply to all plane reflecting surfaces; but there are other sorts of mirrors, whose effects are of a more interesting nature, and which we must hasten to describe—we allude to those whose surfaces are either convex or concave.
Curved mirrors are made of a great variety of shapes, but for the present we shall only describe those which are spherical. Spherical mirrors may of course be either concave or convex.
Fig. 18.—Concave Mirror.
Suppose the arc M N (fig. 18) to be movable round the point O, this revolution will describe the surface of the mirror. The central point C of the hollow sphere of which the mirror forms part, is called the centre of curvature, the line O L the principal axis. By remembering these very simple definitions, we shall be able to understand the action of these mirrors without the slightest difficulty.
To understand how the rays of light are reflected from the surface of the mirror N M at the point F, which is called the focus, we have only to consider the mirror as consisting of an infinite number of facets, all inclined towards that particular point, and forming by reason of their immense numbers a regular spherical surface. In considering the mirror from this point of view, we can immediately see that, on account of the inclination of the supposed facets, the rays that they receive are all reflected back again at the same point; and it may be proved geometrically, that when the incident rays are parallel the focus will be situated somewhere on the line O C, its position depending on the curvature of the mirror.
If, therefore, we receive on a spherical mirror a pencil of sunlight, the rays which compose it may be regarded as parallel, the sun being at so great a distance from the earth; it follows that these rays will all be reflected together in a particular point, viz., at F, and if any object be placed there it will be illuminated with great brilliancy. The laws governing the reflection of heat being nearly similar to those regulating the action of light, the rays reflected from a burning body will ignite any inflammable substance placed at the point F. The focus for parallel rays is called the principal focus of a mirror. Having described the effects of parallel rays, let us now see what happens when the source of light is close to the mirror. If it is placed at a very small distance, the luminous rays are divergent instead of parallel, and their meeting point becomes changed in accordance with the laws laid down at the beginning of this chapter. That is to say, the focus will approach more or less to the centre of curvature C, according as the source of light is placed nearer to or further from the mirror; consequently, in the case of the candle in fig. 19, instead of uniting at F, the rays will meet at f, a point situated somewhat nearer the mirror than the principal focus. If, instead of placing the light at A, we place it at f, we shall find the rays will be concentrated at the point A. Thus the foci are consequently related to each other, and are hence called conjugate foci. It will be readily seen that a spherical mirror may have an infinite number of conjugate foci, according to the distance of the source of light. It is also clear, that if we cause the light to approach the mirror, the focus will also approach it.
Fig. 19.—Conjugate Foci.
Continuing our experiment, we shall find that when the candle passes the principal focus so as to be between it and the mirror, the reflected rays first become parallel and then divergent, and cannot consequently produce any focus beyond the mirror, but are reflected in the way shown in fig. 20.
In experimenting on the plane mirror, we imagined we saw the object at a certain distance behind it; the same thing happens when we see ourselves reflected in a concave mirror, and the particular point at which we suppose we see our reflection is called the virtual focus.
Fig. 20.—Virtual Focus.
If instead of a candle we place our head before a concave mirror, we shall see ourselves magnified as in fig. 21.
Fig. 21.—Concave Mirror.
We shall easily see how this happens by tracing the paths of the rays in fig. 22.
Fig. 22—Magnifying effect of Concave Mirrors
The rays, for instance, which proceed from the forehead at the point a are reflected from the point o to the
Fig. 23.—The Reversal of real Images. eye in such a way as to appear to proceed from a point beyond the mirror, A. In the same manner the rays reflected from the chin appear to take their origin from the point B. If, on the other hand, we place ourselves at a distance from the principal focus, we shall produce a reversed and diminished image of our face. This image is not illusory, like the preceding ones, but is real, and may be received upon a screen, as shown in fig. 23.
We may easily follow the path of the rays as shown in the figure, and we shall see that the rays forming the images of the church-tower and the terrace below, cross at a certain point.
Convex mirrors produce precisely opposite effects, and give a diminished image instead of a magnified one, as may be perceived on examining fig. 24.
Fig. 24.—Diminishing power of Convex Mirrors.