In every plain mirror, the image is always equal to the object, at what distance soever it may be placed; and as the mirror is only at half the distance of the image from the eye, it will completely receive an image of _twice_ its own length. Hence a man six feet high may view himself completely in a looking glass of three feet in length, and half his own breadth; and this will be the case at whatever distance he may stand from the glass. Thus, the man AC (fig. 17) will see the whole of his own image in the glass AB, which is but one half as large as himself. The rays from the head pass to the mirror in the line AA, perpendicular to the mirror, and are returned to the eye in the same line; consequently, having travelled twice the length AA, the man must see his head at B. From his feet C rays will be sent to the bottom of the mirror at B; these will be reflected at an equal angle to the eye in the direction BA, as if they had proceeded in the direction DBA, so that the man will see his foot at D, and consequently his whole figure at BD.
A person when looking into a mirror, will always see his own image as far beyond the mirror as he is before it, and as he moves to or from it, the image will, at the same time, move towards or from him on the other side; but apparently with a double velocity, because the two motions are equal and contrary. In like manner, if while the spectator is at rest, an object be in motion, its image behind the mirror will be seen to move at the same time. And if the spectator moves, the images of objects that are at rest will appear to approach, or recede from him, after the same manner as when he moves towards real objects; plane mirrors reflecting not only the object, but the distance also, and that exactly in its natural dimensions--The following principle is sufficient for explaining most of the phenomena seen in a plane mirror, namely;--_That the image of an object seen in a plane mirror, is always in a perpendicular to the mirror joining the object and the image, and that the image is as much on one side the mirror, as the object is on the other_.
_Reflection by Convex and Concave Mirrors._
Both convex and concave mirrors are formed of portions of a sphere. A convex speculum is ground and polished in a _concave_ dish or tool which is a portion of a sphere, and a concave speculum is ground upon a convex tool. The inner surface of a sphere brings parallel rays to a focus at _one fourth_ of its diameter, as represented in the following figure, where C is the centre of the sphere on which the concave speculum AB is formed, and F the focus where parallel rays from a distant object would be united, after reflection, that is, at one half the radius, or one fourth of the diameter from the surface of the speculum. Were a speculum of this kind presented to the sun, F would be the point where the reflected rays would be converged to a focus, and set fire to combustible substances if the speculum be of a large diameter, and of a short focal distance. Were a candle placed in that focus, its light would be reflected parallel as represented in the figure. These are properties of concave specula which require to be particularly attended to in the construction of reflecting telescopes. It follows, from what has been now stated, that if we intend to form a speculum of a certain focal distance,--for example, two feet, it is necessary that _it should be ground upon a tool whose radius is double that distance_, or four feet.