From what has been stated in relation to concave mirrors it will be easily understood how they make such powerful burning-glasses. Suppose the focal distance of a concave mirror to be twelve inches, and its diameter or breadth twelve inches. When the sun’s rays fall on such a mirror, they form an image of the sun at the focal point whose diameter is found to be about one-tenth of an inch. All the rays which fall upon the mirror are converged into this small point; and consequently their intensity is in proportion as the square of the surface of the mirror is to the square of the image. The squares of these diameters are as 14,400 to 1; and consequently the density of the sun’s rays, in the focus, is to their density on the surface of the mirror as 14,400 to 1. That is, the heat of the solar rays in the focus of such a mirror will be fourteen thousand four hundred times greater than before—a heat which is capable of producing very powerful effects in melting and setting fire to substances of almost every description.
Were we desirous of forming an image by a concave speculum which shall be exactly equal to the object, the object must be placed exactly in the centre; and, by an experiment of this kind, the centre of the concavity of a mirror may be found.
In the cases now stated, the images of objects are all formed in the front of the mirror, or between it and the object. But there is a case in which the image is formed behind the mirror. This happens when the object is placed between the mirror and the focus of parallel rays, and then the image is larger than the object. In fig. 23, GF is a concave mirror, whose focus of parallel rays is at E. If an object OB be placed a little within this focus, as at A, a large image IM will be seen behind the mirror, somewhat curved and erect, which will be seen by an eye looking directly into the front of the mirror. Here the image appears at a greater distance behind the mirror than the object is before it, and the object appears magnified in proportion to its distance from the focus and the mirror. If the mirror be one inch focal distance, and the object be placed eight-tenths of an inch from its surface, the image would be five times as large as the object in length and breadth, and consequently twenty-five times larger in surface. In this way small objects may be magnified by reflection, as such objects are magnified by refraction, in the case of deep convex lenses. When such mirrors are large, for example six inches diameter, and eight or ten inches focal distance, they exhibit the human face as of an enormous bulk. This is illustrated by the following figure. Let C N, Fig. 24, represent the surface of a concave mirror, and A a human face looking into it, the face will appear magnified as represented by the image behind the mirror D Q. Suppose a ray A C proceeding from the forehead, and another M N from the chin; these rays are reflected to the person’s eye at O, which consequently sees the image in the lines of reflection O D, O Q, and in the angle D O Q, and consequently magnified much beyond the natural size, and at a small distance behind the mirror.
figure 23.
figure 24.
If we suppose the side T U to represent a convex mirror, and the figure D Q a head of an ordinary size, then the figure A will represent the diminished appearance which a person’s face exhibits, when viewed in such a mirror. It will not only appear reduced, but somewhat distorted; because from the form of the mirror, one part of the object is nearer to it than another, and consequently will be reflected under a different angle.
The effect we have now mentioned as produced by concave mirrors, will only take place when the eye is nearer the mirror than its principal focus. If the spectator retire beyond this focus—suppose to the distance of five or six feet, he will not see the image behind the mirror; but he will see his image in a diminished form, hanging upside down, and suspended in the air, in a line between his eye and the mirror. In this case, his image is formed before the mirror as represented at IM fig. 22. In this situation, if you hold out your hand towards the mirror, the hand of the image will come out towards your hand, and, when at the centre of concavity, it will be of an equal size with it, and you may shake hands with this aerial image. If you move your hand farther, you will find the hand of the image pass by your hand, and come between it and your body. If you move your hand towards either side, the hand of the image will move towards the other side; the image moving always in a contrary direction to the object. All this while the by-standers, if any, see nothing of the image, because none of the reflected rays that form it can enter their eyes.—The following figure represents a phenomenon produced in the same manner. A B is a concave mirror of a large size; C represents a hand presented before the mirror, at a point farther distant than its focus. In this case, an inverted image of the hand is formed which is seen hanging in the air at M. The rays C and D go diverging from the two opposite points of the object, and by the action of the mirror, they are again made to converge to points at O and S where they cross, form an image, and again proceed divergent to the eye.10
figure 25.
In consequence of the properties of concave mirrors, now described, many curious experiments and optical deceptions have been exhibited. The appearance of images in the air, suspended between the mirror and the object, have sometimes been displayed with such dexterity and an air of mystery, as to have struck with astonishment those who were ignorant of the cause. In this way birds, flying angels, spectres and other objects have been exhibited, and when the hand attempts to lay hold on them, it finds them to be nothing, and they seem to vanish into air. An apple or a beautiful flower is presented, and when a spectator attempts to touch it, it instantly vanishes, and a death’s head immediately appears, and seems to snap at his fingers. A person with a drawn sword appears before him, in an attitude as if about to run him through, or one terrific phantom starts up after another, or sometimes the resemblances of deceased persons are made to appear, as if, by the art of conjuration, they had been forced to return from the world of spirits. In all such exhibitions, a very large concave mirror is requisite, a brilliant light must be thrown upon the objects, and every arrangement is made, by means of partitions, &c., to prevent either the light, the mirror, or the object from being seen by the spectators. The following representation (fig. 26.) shows one of the methods by which this is effected: A is a large concave mirror, either of metal or of glass, placed on the back part of a dark box, D is the performer, concealed from the spectators by the cross partition C; E is a strong light, which is likewise concealed by the partition I, which is thrown upon the actor D, or upon any thing he may hold in his hand. If he hold a book, as represented in the figure, the light reflected from it will pass between the partitions C and I to the mirror, and will be reflected from thence to Z, where the image of the book will appear so distinct and tangible, that a spectator looking through the opening at X, will imagine that it is in his power to take hold of it. In like manner, the person situated at D, may exhibit his own head or body—a portrait, a painting, a spectre, a landscape, or any object or device which he can strongly illuminate.
figure 26.
figure 27.
figure 28.
There is another experiment, made with a concave mirror, which has somewhat puzzled philosophers to account for the phenomena. Take a glass bottle AC, (fig. 27) and fill it with water to the point B; leave the upper part BC empty, and cork it in the common manner. Place this bottle opposite a concave mirror, and beyond its focus,