Concave mirror

“ Plane mirrors, as we have seen, reflect objects upright and symmetrical, reversing only the sides. Concave mirrors reverse them, and if they are not placed exactly in the proper focus, distort them by making one portion appear smaller than the other; while convex mirrors reflect them in an upright position, but also similarly slightly distorted. But when the mirror is not a portion of a sphere, like those whose properties we have been considering, the distortion is increased to so great an extent as to deform the object so that it is difficult to recognise its nature from its reflection. ”

“ Instead of being plain, mirrors may be either concave or convex. A concave mirror is hollowed out in conformity with a small section of the surface of a sphere. If a piece of glass be cut out of a hollow sphere, the inner side of it will show the surface of a concave, and the outer side, the surface of a convex mirror. ”

“ What is there in this structure that can represent a concave mirror? Yet no one can look at the sight I am speaking of, without feeling certain that the optical process is one of concave reflection and convergence of the rays; and that the reflecting surface is in the interior of the globose compound eye. The reflection is seen whatever part of the eye is opposite the light, (provided it be facetted of course) but is most full direct in front, where no unfacetted portion can be seen. ”

“ Take a concave mirror of the diameter of 40 inches, and three in concavity, made by cementing pieces of looking-glass on a wooden mould. The focus will be three feet six inches or so from the mirror.
The image of a person standing before it will be so vivid and seemingly solid that it will terrify even a strong-minded experimentalist. ”

“ Here a convex lens produces a distant, and therefore magnified image of a near transparent object, which is strongly enlightened by a lamp placed behind it; a concave mirror is generally put behind the lamp to throw as much of the light as possible on the object, which is some group of figures painted on a glass slide, and is inverted so that the image may be cast in an erect position, on a wall or a white sheet, at a proper distance. ”

“ If the door of the room opens towards the mirror, and a spectator unacquainted with the properties of concave mirrors should enter the apartment, the person would be greatly startled to see flames apparently playing over the surface of the table, whilst another spectator might enter from another door and see nothing but a long beam of light, rendered visible by the floating particles of dust. To give proper effect to this experiment the concave mirror should be large, and no other light must illuminate the room except that from the fire. ”

“ The rays of light A B are first reflected from the concave mirror M on to the surface of the small plane mirror m, which is placed at an angle of 45°, and reflects them as far as the point A ́ B ́, where they form the image to be magnified by the eye-glass. ”

“ The image of a straight object, placed either parallel or oblique to the mirror is seen curved in the mirror; because the different points of the object are not all at an equal distance from the surface of the mirror. 5. Concave mirrors have a real focus where an image is actually formed; but convex specula have only a virtual focus, and this focus is behind the mirror ”

“ The effects produced by the action of concave mirrors may be produced with just as much facility by convex lenses. If a body is placed in a focus of a lens which receives the direct rays of the sun, the heat as well as the light will be concentrated at one point; and if the object is combustible, it will take fire sooner or later, according to the size of the lens. All the experiments mentioned by Buffon as being produced by a concave mirror are equally obtainable with a concave lens. ”

“ The direct light of the lamp G, as well as that reflected by the mirror and passing through the lens c, is so concentrated as to project a brilliant beam of light through the painted slide, which being in the conjugate focus of the large plano-convex lens d, the pictures on the glass are refracted in a magnified form on the white cloth P Q.
The magic lantern, therefore, consists of a box to hold the lamp, a concave mirror, and a convex lens to concentrate the light on the slide, and a second convex lens to throw the image on the screen. ”

“ By all means they must improve their mirrors. Czermak, the Professor of Physiology at Pesth, taking an example from the instrument used in examining the eye, the ophthalmoscope, had recourse to a concave mirror which concentrated the light. ”

“ The Reflector.—In a reflecting telescope, the object-glass of the refractor is replaced by a concave mirror. In order that such a mirror may reflect all the rays from a star to a single point, its concave surface must be part of a paraboloid of revolution, that is, a surface produced by the revolution of a parabola on its axis. If a spherical surface be employed, all the rays will not be reflected to a single point and the images which it gives will be ill-defined. ”

“ The Perspective Mirror.
Provide a box, A B C D, Fig. 24, of about two feet long, 15 inches wide, and 12 inches high. At the end A C, place the concave mirror, the focus of whose parallel rays is 18 [Pg 125] inches from the reflecting surface. At I L place a pasteboard, blacked, in which a hole is cut, sufficiently large to see on the mirror H the object placed at B E F D. Cover the top of the box, from A to I, close, that the mirror H may be entirely darkened. The other part, I B, must be covered with glass, under which is placed a gauze, or oiled paper, to prevent the inside from being seen. ”

“ 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 100 arrangement is made, by means of partitions, &c., to prevent either the light, the mirror, or the object from being seen by the spectators. ”

“ In most cases in which the reflexion is made by a concave mirror, the rays proceeding from the various points of an object are made to converge, and actually meet in points constituting the image, and afterwards diverge from those points, as they would from a real surface placed there, so as to make it visible. ”

“ The account is not very clear, but seems to imply the use of a concave mirror rather than a lens, which might be suggested by the word orbem. He refers to Maurolycus’ work with concave specula.
We now come to Giovanni Battista della Porta, whose account of the camera obscura in the first edition of the Magia Naturalis, in four books (1558, lib. iv. cap. 2) , is very similar to Caesariano’s—a darkened room, a pyramidal aperture towards the sun, and a whitened wall or white paper screens, but no lens. ”

“ The introduction of the magic lantern provided the magicians of the seventeenth century with a very powerful instrument with which to continue their deceptions. The use of the concave mirror, which does not appear to have had any accessories worth speaking of, required a separate apartment, or at least a hiding-place of some sort that was difficult to discover under ordinary circumstances ”

“ In Figure 78 we have drawn the arrow and the image it would produce in the mirror. If the mirror forms a section of a sphere, the object reflected will appear reduced in size in all directions. If the mirror forms merely a section of a cylinder, a person standing in front of it will appear very much shorter than natural but of full width thus presenting a ridiculous appearance. Convex and concave mirrors are often combined and if properly set, a person standing in front of one may see himself either very much elongated or shortened. ”

“ But we will first devote a short time to the curious historical facts connected with the principle of the magic lantern which took place long before the modern invention of this instrument by Father Kircher.
Brewster says, when treating of this subject, that there can be little doubt that the concave mirror was the principal instrument used in connexion with the pretended apparitions of the gods and goddesses in the ancient temples. In the meagre history of these apparitions that has come down to us, we can easily perceive the traces of an optical illusion. ”

“ The flat mirrors are of silvered glass, and are used with the silvered side toward the light, to avoid the double image produced when reflection from both sides of a parallel plate of glass is permitted. The large concave mirror happens to be of speculum metal, but it can be repolished if necessary by means of a four inch polisher, passed in succession over every chord of the face. A yellow film of tarnish easily accumulates on metal specula if they are not carefully kept, and decreases their photographic power seriously. ”

“ Nearly the whole surface of the mirror should be equally illuminated; this may be tested by temporarily placing upon it a card or piece of white paper. Parallel rays can also be obtained from the concave mirror, if the light is placed about 21⁄2 inches from it. Dark-ground illumination is not suitable for very transparent objects—that is, unless there is a considerable difference in their index of refraction, or they are pervaded by air-cells. ”

“ We know that what renders common reflecting mirrors most useless for experiments is, that they burn almost always upwards, and that we are greatly embarrassed to find means to suspend or support to their focus matters to be melted or calcined. By means of my mirror we burn concave mirrors downwards, and with so great an advantage that we have what degree of heat we please ”

“ Explanation.—Behind a partition, A B (Fig. 140) , place a concave mirror E F, ten inches diameter, and at a distance three-fourths from its centre, somewhat 216inclined. In the partition cut a square or circular opening, about eight inches wide, directly opposite the mirror. Behind have a light to illuminate any object at C, without shining on the mirror or being visible at the opening. Behind the aperture and beneath it place inverted the object of which a phantom is to appear. ”

“ In the Newtonian reflector the image is rejected out at the side of the tube by a flat surface placed at 45° with the optical axis of the large concave.7 If this secondary mirror is either convex or concave, it modifies the image injuriously, causing a star to look like a cross, and this though the curvature be so slight as hardly to be perceptible by ordinary means. ”

“ Behind it is a concave mirror set on the floor at an angle in an opening in the wall. Within the other room an arm and hand of wax, holding a dagger, are mounted so as to descend, while brilliantly illumined, towards the concave mirror.
A person can show his or her face instead of his arm 223or the false limb, and something rather laughable than terrifying is recommended for such experiments to a juvenile auditory.
THE GHOST ILLUSION. In The Secret Out the explanation of “The Witch of Endor” trick showed how spectres may be made to appear by aid of the magic lantern. ”

“ Let (fig. 6) be a section of a concave spherical mirror through its centre and luminous point . If a ray, say , meet the surface, it will be reflected along , which is coplanar with and the normal at , and makes the angle . Hence . This expression may be simplified if we assume to be very close to , i.e. that the ray is very slightly inclined to the axis. Writing for , we have ; and calling , and , this reduces to . This formula connects the distances of the object and image formed by a spherical concave mirror with the radius of the mirror. ”

“ It was the first reflector in which only a single mirror was employed. In the "Gregorian" form, the focussed rays are, by a second reflection [Pg 110] from a small concave [309] mirror, thrown straight back through a central aperture in the larger one, behind which the eye-piece is fixed. The object under examination is thus seen in the natural direction. ”

“ In short, those who examine my theory, and shall have seen the effect of my mirror, I think will be convinced the mode I have used was the only one possible to succeed to burn far off, for, independant of the physical difficulty of [214] making large concave, spherical, parybolical mirrors, or of any other curvature whatsoever, regular enough to burn at 150 feet distance, we shall easily be convinced that they would not produce but nearly as much effect as mine, because the focus would be almost as broad ”

“ The ancients, not having the means of either casting or grinding such enormous mirrors, must have constructed them of a large number of small ones, so arranged that the images of the sun reflected by them would all fall in the same place, or nearly so. In this case, the larger the number of mirrors, the greater would be the burning effect. In order to explain the reflection of rays incident upon the surface of concave mirrors, we supposed them to consist of an immense number of plane mirrors placed in a curve, so that the reflected rays might all meet in one point ”

“ Oriental stories of magic mirrors have been current from the middle ages, most of them wholly childish and absurd. But along with these there have existed accounts, of a more reliable character, of mirrors which are capable of reflecting, in a beam of light that falls on their face, the pattern which they carry on their back. This singular property is no myth, though the true explanation of the phenomenon was long unknown. When first seen, the phenomenon is so startling that it seems almost incredible. You take the mirror into your hand and examine it. ”