Mirrors or Specula, may be distinguished into three kinds, plane, concave, and convex, according as they are bounded by plane or spherical surfaces. These are made either of metal or of glass, and have their surfaces highly polished for the purpose of reflecting the greatest number of rays. Those made of glass are foliated or quicksilvered on one side; and the metallic specula are generally formed of a composition of different metallic substances, which, when accurately polished, is found to reflect the greatest quantity of light. I shall, in the first place, illustrate the phenomena of reflection produced by plane-mirrors.
When light impinges, or falls, upon a polished flat surface, rather more than the half of it is reflected, or thrown back in a direction similar to that of its approach; that is to say, if it fall perpendicularly on the polished surface, it will be perpendicularly reflected; but if it fall obliquely, it will be reflected with the same obliquity. Hence, the following fundamental law, regarding the reflection of light, has been deduced both from experiment and mathematical demonstration, namely, that the angle of reflection is, in all cases, exactly equal to the angle of incidence. This is a law which is universal in all cases of reflection, whether it be from plane or spherical surfaces, or whether these surfaces be concave or convex, and which requires to be recognized in the construction of all instruments which depend on the reflection of the rays of light. The following figure (fig. 14) will illustrate the position now stated.
Let AB represent a plane mirror, and CD a line or ray of light perpendicular to it. Let FD represent the incident ray from any object, then DE will be the reflected ray, thrown back in the direction from D to E, and it will make with the perpendicular CD the same angle which the incident ray FD did with the same perpendicular, that is, the angle FDC will be equal to the angle EDC, in all cases of obliquity. The incident ray of light may be considered as rebounding from the mirror, like a tennis ball from a marble pavement, or the wall of a court.
figure 14.
In viewing objects by reflection we see them in a different direction from that in which they really are, namely, along the line in which the rays come to us last. Thus, if AB (fig. 15) represent a plane mirror, the image of an object C appears to the eye at E behind the mirror, in the direction EG, and always in the intersection G of the perpendicular CG, and the reflected ray EG—and consequently at G as far behind the mirror, as the object C is before it. We therefore see the image in the line EG, the direction in which the reflected rays proceed. A plane mirror does not alter the figure or size of objects; but the whole image is equal and similar to the whole object, and has a like situation with respect to one side of the plane, that the object has with respect to the other.
figure 15.
Mr. Walker illustrates the manner in which we see our faces in a mirror by the following figure (16). AB represents a mirror, and OC, a person looking into it. If we conceive a ray proceeding from the forehead CE, it will be sent to the eye at O, agreeably to the angle of incidence and reflection. But the mind puts CEO into one line, and the forehead is seen at H, as if the lines CEO had turned on a hinge at E.—It seems a wonderful faculty of the mind to put the two oblique lines CE and OE into one straight line OH, yet it is seen every time we look at a mirror. For the ray has really travelled from C to E, and from E to O, and it is that journey which determines the distance of the object; and hence we see ourselves as far beyond the mirror as we stand from it. Though a ray is here taken only from one part of the face, it may be easily conceived that rays from every other part of the face must produce a similar effect.
figure 16.
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.
figure 17.
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.
figure 18.
Properties