THE PROPERTIES OF MIRRORS.
Almost every one in his younger days has possessed
and broken that pretty instrument known as the kaleidoscope.
His researches into its construction no doubt
taught him that it consisted of a cylindrical tube in tin
or cardboard, with a moveable cap at one end and a
small hole at the other. In the interior of the tube
were found three long glasses, blackened on the back,
placed at an angle, and kept in position by pieces of
cork. The moveable cap was provided with two circular
pieces of glass, one ground and the other transparent,
between which were placed a number of pieces
of coloured glass. On holding the instrument up to
the light and looking through the eye-hole, a beautifully
coloured star was seen whose form and hue
changed by simply shaking the tube.
The kaleidoscope was invented by Sir David Brewster, and is exceedingly simple in principle. We all know that if a luminous object, such as a taper, is placed before a mirror, it gives forth rays of light in all directions. Amongst these luminous rays, those that fall on the surface of the mirror are, of course, reflected in such a manner that the angle of reflection is equal to the angle of incidence. If another mirror be placed at right angles to the first, and an object be put in the angle, the image of it will be multiplied four times. If the angle be diminished to 60°, six reflections will be seen, and so on. A symmetrical figure is constantly obtained, forming in one case a cross composed of four similar portions; in the other a triple star, the halves of each ray being similar. It is the symmetry of the figure that gives the pleasing effect. In the ordinary kaleidoscope the angle made by the reflecting surfaces is thirty degrees, and a star of six rays is formed, the halves of each ray being alike. The figures formed in the kaleidoscope are simply endless; and if the space between the glasses in the moveable cap be filled with bits of opaque as well as transparent substances, the varieties of light and shade may be added to those of colour. It was at one time the fashion to copy the images formed in the kaleidoscope as paterns for room papers, muslins, curtains, shawls, and other similar fabrics, but thanks to the spread of artistic taste in this country the decorative designer now relies more on his own talent than any aid he may receive from optical instruments.
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. We all know the distortion that our face undergoes when reflected from the shining surface of a teapot or spoon, and the cylindrical mirrors that hang in the shop windows of many opticians are the source of much amusement to the passers by, whose physiognomies are shown to them either lengthened to many times their natural size, or widened to an extent that is ludicrously hide-ous, according to the position in which the mirror is hung. Such distortions are known to opticians as anamorphoses, from two Greek words signifying the destruction of form; and distorted drawings used to be sold at one time which when reflected from the surface of the cylindrical mirror, became perfectly symmetrical. Anamorphic drawings may be also made, which when looked at in the ordinary manner appear distorted, but when viewed from a particular point have their symmetry restored to them. With a little knowledge of drawing, it is not difficult to produce these in great variety.
Suppose the portrait in fig. 62 to be divided horizontally and vertically by equidistant lines comprehended within the square A B C D.
Fig. 62.
Upon a second piece of paper draw the figure shown in fig. 63 in the following manner. Draw the horizontal line a b equal to A B (fig. 62,) and divide it into the same number of parts. Through the centre draw a perpendicular line to V, and cross it by a line e d parallel to a b. Lastly, draw V S horizontal to e d. The length of the two lines e V and S V is quite arbitrary, but the longer you make the former in proportion to the latter the greater will be the distortion of the drawing Now draw the lines V 1, V 2, V 3, and V 4, and join S to a. Wherever S a crosses the divisions 1, 2, e 3, 4, and b, draw a horizontal line, parallel of course with a b. You will thus have a trapezium a b c d divided into as many spaces as the square A B C D in fig. 62, and it now remains to fill them in with similar portions of the figure. Thus, for instance, the nose is in the fourth vertical division, starting from the left, and in the third and fourth counting from the top; in order, therefore, to make it occupy so lengthened a space it must be considerably distorted by the pencil. It will be readily seen also that the more numerous the spaces into which the square is divided, the easier it will be to draw the distorted picture. It is by this means that the anamorphosis shown in fig. 63 has been drawn.
The next thing to do is to find the point of view from which we can see the figure in its natural proportions. This will be found to be at a distance above the point V equal to the line V S. In order to complete the experiment it is simply necessary to place the distorted picture in a horizontal position, and fix a piece of cardboard vertically at the point V. If a hole be punched in it at a distance from V equal to S, and the drawing be looked at through it, the whole of the parts will fall into symmetry immediately.
The experiment may be tried first with fig. 63, the hole being made rather large, and the eye placed at a distance of from 3 to 4 inches.
It would be difficult, without having recourse to geometrical formulæ, to explain how it happens that by placing the eye at a particular point the distorted lines of the drawing become symmetrical; but perhaps a mechanical demonstration will help to make this difficult subject a little plainer.
Draw in outline any figure upon a piece of cardboard, and make a series of pin-holes along the most prominent lines of the drawing, taking care that they are pretty
Fig. 63.—Anamorphosis.
close together. Place the perforated card in a vertical position on a sheet of paper, so that the rays from a candle or lamp may fall, on the flat surface beneath. On looking at the luminous figure formed from the drawing, you will find that it is as much distorted as the lady's head in fig. 63, and that the lower you place the candle
the greater will be the deformity. You may if you
please, trace the luminous figure on the paper, and the
result will appear distorted when looked at in the ordinary
manner, but symmetrical when viewed from the
point at which the flame of the candle was placed.
In the foregoing experiments we have spoken of the anamorphic drawings as being placed in a horizontal position, but they may be looked at just as well vertically, the card with the hole being in this instance horizontal. It is also not necessary that the point of sight (V, fig. 63) should be in the centre of the picture; it may be placed at one side or the other, care being taken to draw all the divisional lines so that they meet at this particular spot. A few experiments with a candle and a perforated figure will soon show the student how to accomplish this.
Anamorphoses by reflection may be prepared, if this principle is carried out, which appear a mass of confused lines until they are reflected in a cylindrical mirror. Formerly opticians were accustomed to construct anamorphoses which became symmetrical pictures when viewed in a conical mirror; but the fashion for such toys appears to have gone out. Such drawings were extremely difficult to make, and the mirrors, having to be ground and polished with great care, were very expensive.
Some experimentalists have carried the subject so far that, by looking at the drawing of an object in particular positions, it changed into quite a different subject. In the cloister of an abbey that once existed in Paris, there were two anamorphoses of this kind. They were the work of a certain Father Niceron, who has left behind him a treatise in Latin on optical wonders, entitled Thaumaturgus Opticus, which contains a long essay on anamorphoses. One of these pictures repre-sented St. John the Evangelist writing his Gospel; the other Mary Magdalene. When looked at in the ordinary manner, they appeared to be landscapes; but when the observer placed himself in a particular position, they changed into the figures we have mentioned.