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.