ON KALEIDOSCOPES IN WHICH THE EFFECT IS PRODUCED BY
TOTAL REFLEXION FROM THE INTERIOR SURFACES OF
TRANSPARENT SOLIDS.
When light is incident upon the most perfectly polished metals, a very
considerable quantity of it is absorbed, and even when the reflexion is
made at the greatest obliquities, there is a very manifest difference
in the intensity of the direct and the reflected pencil. In the total
reflexion of light from the second surfaces of transparent bodies, the
loss of light is very inconsiderable, and the reflexion is made with a
degree of brilliancy far surpassing that of the most resplendent metals.
[Illustration: FIG. 49.]
In constructing a Kaleidoscope upon this principle, we must procure
a piece of glass entirely free from veins, and cut it into the form
shown in Fig. 49.[7] The two surfaces =B O E=, =A O E=, must be
inclined at an angle which is the even aliquot part of a circle. They
must be ground perfectly flat and highly polished, and the junction
=O E= must be made as fine as possible. The upper surface =A B E=
should be rough-ground, and the side =A B O=, and the side at =E=,
should be parallel and well polished. If the glass is colourless and
good, the eye, when placed at =E=, will see the very same appearance
as in the simple Kaleidoscope; and objects placed at =A B O= will be
arranged into the same beautiful figures. The only defects attending
this form of the Kaleidoscope, are the loss of light occasioned by its
passing through a mass of solid glass, not perfectly transparent, and
the difficulty of obtaining a perfect junction of the two reflecting
planes. The first of these evils is, however, counterbalanced by
the great intensity of the light which suffers total reflexion; and
the second does not exist when the Kaleidoscope is intended to give
rectilineal or annular patterns.
[7] When this chapter was written (1818), it was very difficult to
procure glass sufficiently homogeneous for this purpose: but it can now
be procured from the Glass Works of Messrs. Chance & Co., at Smethwick,
near Birmingham.
In the construction of instruments of this kind, it is necessary to
make the prism of glass longer than the distance at which the eye
can see objects with perfect distinctness; that is, if the eye is
capable of seeing objects distinctly at the distance of five inches,
it will not perceive the same objects distinctly when they are placed
at the end of a prism of glass five inches long. This singular effect
arises from a property of plain lenses or pieces of plain glass, in
consequence of which, they cause divergent rays to diverge from a point
nearer the lens or plate, than that from which they radiated. It will
therefore be more convenient, for many reasons, to make the glass prism
only two or three inches long, and obtain distinct vision by means
of a lens placed at the eye-end of it; but, for the reason already
mentioned, the focal length of the lens must be less than the length of
the glass prism. The lens may even be joined to the prism, by grinding
the eye-end into a spherical form, but the degree of convexity must be
calculated upon the principles already stated.
The solid form of the Kaleidoscope is peculiarly fitted for polycentral
instruments, as we have only to polish the side, which would otherwise
have been left rough, the prism being supposed to be cut to the angles
which are necessary to give symmetrical forms, according to the
principles stated in Chapter XIII.