1902 Encyclopedia > Kaleidoscope

## Kaleidoscope

KALEIDOSCOPE. This, as the name implies, is an instrument by means of which beautiful forms may be seen. It was invented by Sir David Brewster about 1815,—the idea of the instrument having occurred to him some time before while he was engaged with experiments on the polari-zation of light by reflexion. When it first appeared it attracted almost universal attention. This arose from the extreme beauty of the forms which it presented, their end-less variety and perfect symmetry, as well as the readiness with which one beautiful form could be converted into another. The construction of the instrument was so simple, too, that almost any one could make it; and, in conse-quence, the patent originally taken out by Brewster was persistently evaded ; kaleidoscopes were made by the hun-

dred, and sold in almost every toy-shop. Large cargoes of them were sent abroad; and it is stated that no fewer than two hundred thousand were sold in London and Paris in the space of three months. Besides being of essential service in the art of the designer, the kaleidoscope consti-tutes a very useful piece of philosophical apparatus, as it illustrates, in a very beautiful way, the optical problem of the multiplication of images produced by reflexion when the object is placed between two plane mirrors inclined to each other at a definite angle.
The general principle of the instrument will be easily understood from the following description and figures.
f? A

X p
[
y, 0
x, Y
Pi
1. Let OA, OB (fig. 1) be the sections of two plane mirrors placed
perpendicular to the plane of the paper and inclined to each other
at a right angle. Let P be a luminous point, or object, placed
between them. According to
the general law of the reflexion
of light from plane mirrors,
the image of P formed by the
mirror OA will be as far behind
OA as P is in front of it; that
is, the image of P is P1; where
PX = P!X, the line PP1 being
perpendicular to OA. Now
Pj may be regarded as a new-
object placed before the mirror
OB, and hence the image of
Pi formed by OB will be P,
where PJYJ = P2Yj. Similarly
the image of P formed by OB
will be P/, where PY-P/Y,
and the image of P/ formed by Fig- 1.
OA will also be at a point such that P/Xj = 7.2Xlt that is, the two last formed images will coincide. Hence we have three images placed symmetrically about 0, constituting, with the object P, a symmetrical pattern of four luminous points placed at the corners of a rectangle.

2. Let the mirrors OA and OB (fig. 2) be inclined to each other
at any angle a, and let P be the object placed between them. With
centre 0 and radius OP describe a circle. Evidently the images
formed by successive reflexions from the mirrors will all lie on the
eircumference of this circle. We shall denote the images formed
by a first reflexion at OA,
second at 0 B, third at OA,
and so on, by the symbols
Pj, P2, P3 respectively ;
and the images formed by
a first reflexion at OB,
yeeond at OA, third at OB,
and so on by P/, P2', P3'
respectively. Draw PP1
perpendicular to OA,
perpendicular to OB, P2P3
perpendicular to AO pro-
duced, and P3P4 perpen-
dicular to BO produced.
Then Pj, P2, P3, P4 are the .
first set of images formed.
Similarly draw the lines
then Pj'., P2', P3', P4' are the second set of images formed by a first reflexion at OB. Now, when any image falls within the angle vertically opposite to AOB, it is evident that no further reflexion can take"place, as it is behind both mirrors. Hence the number of images formed depends upon the size of the angle AOB and also upon the position of the point P in relation to the mirrors.
When a symmetrical picture is required, it is essential that the two last formed images, that is, P4 and P4' in the figure, should coincide, and we must determine when this will be the case. We shall measure the distances of the several images from P by the arcual distances PP1; &c. Now it is evident that
PiPPi'- 2PA + 2PB = 2AB = 2a.
P2PP2' = P P2 + PP2'=PB + P^ + PA + P/A = PB + PA + AB + P,A + AB + P,'B = 4AB=4a.
P„PP„'=2«a.
Now, when the last formed images coincide, the arcual distance between them must be a whole circumference. Hence if P„ and P„' be the last formed coincident images, we have
P„PP„' = 2»a = 27r.
PoPPa' = 6«.
that is, the mirrors must be inclined to each other
Hence
at an angle whicll is an exact submultiple of two right angles, or, which is the same thing, an even submultiple of 360°.

3. Next suppose that, instead of a point, we put a line as an
object in the angle between the mirrors ; and, first, let us suppose
that the mirrors are inclined to each other at an angle which is an
odd submultiple of 360° (as one-fifth of 360° in fig. 3). OA, OB
are the mirrors, PQ the line
placed between them. The
image of PQ formed by OA
is PQj, that formed by OB
is QPj. The image of PQ-L
formed by OB is PjQj, and
the image of QPj formed by
OA _ is QjPa.' Now it is
P2 and Q2will not, in general,
coincide, and, hence, a sym-
metrical picture of the line
cannot in general be formed
when the angle is an odd
submultiple of 360°. If,
however, the line OP = 0Q,
then the points P2 and Q2
will coincide, and a sym- Fig- 3.
metrical picture of five lines be formed. Secondly, let us suppose that the angle AOB is an even submultiple of 360°. By following the course of the images it will be seen that the last-formed images of the line coincide in all positions of PQ, and hence a symmetric&l figure can, in all cases, be formed.
As the object of the kaleidoscope is to produce symmetrical figures from objects placed in any position between the mirrors, we are necessarily limited to angles which are even submultiples of 360°.

The simple kaleidoscope consists essentially of two plane mirrors EOA and EOB (fig. 4) inclined to each other at an angle which is an even submultiple of 360°. A very common angle in practice is 60°. The mirrors are usually made of two strips of thin flat glass,—the length of each being from 6 to 12 inches, and A the greatest breadth from 1 to 3 inches. The mirrors are first fixed, in any convenient manner, at the proper angle, and then inserted into a cylindrical tube of brass or paper. At the one end of the tube is a small eye-hole opposite the point E, while the other end is closed by what is called the " object box." This consists of a shallow cylindrical box, which fits on to the end of the tube, and contains the objects from whose reflexion the pattern is pro-duced. These objects may consist of petals of differently coloured flowers, scraps of differently coloured paper, or, still better, pieces of coloured glass. Very often the objects consist of small glass tubes filled with differently coloured liquids and then hermetically sealed. These produce a very fine effect. The objects are placed in the box between two circles of thin glass which fit into the box, the one of which is transparent and the other obscured by grinding. When in position the transparent glass is close to the end of both mirrors and fills up the sector AOB, while the other, the obscured one, is fixed into the outer end of the object box. The distance between the two glasses is made as small as possible,—just room enough being left to allow the objects to fall freely by their own weight into any position between the glasses. Suppose now that the angle AOB is 60°, and that the eye is placed at E, a beautiful symmetrical picture of six equal and similar sectors will be seen round the point O; and, by simply turning the tube round, so as to allow the objects to fall into a new position, an endless variety of pictures can be produced. It is important to notice the proper position of the I eye. This should be, as nearly as possible, in the plane

of both mirrors,—first, because in that position only the direct and reflected sectors are all at the same distance from the eye, and, in consequence, no want of symmetry is introduced by the foreshortening of one sector more than another; and, secondly, because in that position the maximum amount of light is reflected to the eye by the mirrors, and, in consequence, the various sectors appear as nearly as possible equally illuminated. Of course a certain amount of light is necessarily lost at each reflexion, and hence there is always a slight difference between the luminosity of the various sectors. However, this is found not to introduce any serious want of symmetry when the instrument is properly constructed.
A modification of the simple kaleidoscope was introduced by Sir David Brewster, whereby the images of large and distant objects can be introduced into the picture. This is effected by removing the object box and replacing it by a tube carrying at its outer end a double convex lens, represented by LL in fig. 5. By a screw adjustment the lens can be so placed as to focus the distant object

Fig. 5.
exactly in the plane of the sector AOB, and so bring its image into the very best position for producing symmetrical patterns. When this instrument is directed towards a tree in full foliage, or towards an arrangement of flowers in full bloom, a very beautiful effect is produced, which can be varied by gradually moving the instrument. This form was called by Brewster the telescopic kaleidoscope.

Another form is called the polyangidar kaleidoscope. (fig. 6). The only essential difference in it is that the mirrors are so ar-ranged that the angle between them can be varied at pleasure. This, being very use-ful for illustrating the theory of the instru-ment, is the form usually found in col-lections of philosophi-cal apparatus.
In all the instruments above described only two mirrors have been employed; but obvious-ly we may have more than two. Suppose we wish to employ three mirrors enclosing a tri-angular opening, and that we also wish to produce perfectly sym-metrical pictures. We are here limited in our choice of angles by the following conditions—first, the sum of the three angles which the mirrors make with each other must be equal to 180°, and, secondly, each angle must be an even submultiple of 360°. By trial it is easily found that the only angles which satisfy these con-ditions are 60°, 60°, 60°; 90°, 60°, 30°; and 90°, 45°, 45°. Hence with three mirrors we must choose one or other of these three sets. The first is that usually chosen.
Suppose similarly we wish to use four mirrors ; then, we must put them either in the form of a square, when all the mirrors are of equal breadth, or in the form of a rectangle, when the opposite mirrors are of equal breadth. It is obvious that in these two cases only will the angle between each pair of mirrors be an even sub-multiple of 360°.
With more than four mirrors kaleidoscopes cannot be constructed so as to give symmetrical forms, since each of the interior angles of a regular polygon of more than four sides must exceed an even sub-multiple of 360°.
See Harris's Optics ; Wood's Optics ; Parkinson's Optics ; Brewster's Treatise on the Kaleidoscope. The last-mentioned contains an account of the application of the instrument to the art of designing. (J. BL.)