The kaleidoscope : $b its history, theory and construction. With its application to the fine and useful arts — John Shaqi
The kaleidoscope : $b its history, theory and construction. With its application to the fine and useful artsBrewster, David
Science
The kaleidoscope : $b its history, theory and construction. With its application to the fine and useful arts
Brewster, David
Kaleidoscopes
Let us now consider what will happen, by removing the object beyond
the plane passing through =A O B=. In this case the pattern will lose
its symmetry from two causes. In the first place, it is manifest, as
already explained, that as the eye is necessarily raised a little above
the point =E=, and also above the planes =A O E=, =B O E=, it must see
through the aperture =A O B= a portion of the object situated below
both of these planes. This part of the object will therefore appear
to project beyond the point, or below the plane where the direct and
reflected images meet. If we suppose, therefore, that all the reflected
images were symmetrical, the whole picture would lose its symmetry in
consequence of the irregularity of the sector =A O B= seen by direct
vision. But this supposition is not correct; for since the image _m
n_, Fig. 3, seen by direct vision does not coincide with the first
reflected images _mnʹ_, _nmʹ_, it is clear that all the other images
will likewise be incoincident, and, therefore, that the figure formed
by their combination must lose its symmetry, and, consequently, its
beauty.
As the eye must necessarily be placed above a line perpendicular to the
plane =A B O= at the point =O=, it will see a portion of the object
situated below that perpendicular continued to the object. Thus, in
Fig. 16, if the eye is placed at _e_ above =E=, and if =M N= is the
object placed at the distance =P O=, then the eye at _e_ will observe
the portion =P Oʹ= of the object situated below the axis =P O E=, and
this portion, which may be called the aberration, will vary with the
height =E _e_= of the eye, and with the distance =O P= of the object.
[Illustration: FIG. 17.]
Let us now suppose =E _e_= and =O P= to be constant, and that a
polygonal figure is formed by some line placed at the point =Q= of the
object =M N=. Then if =P Q= is very great compared with =P Oʹ=, the
polygonal figure will be tolerably regular, though all its angles will
exhibit an imperfect junction, and its lower half will be actually,
though not very perceptibly, less than its upper half. But if =Q=
approaches to =P=, =P Oʹ= remaining the same, so that =P Oʹ= bears a
considerable ratio to =P Q=, then the polygonal figure will lose all
symmetry, the upper sectors being decidedly the largest, and the lowest
sectors the smallest. When =Q= arrives near =P=, the aberration becomes
enormous, and the figure is so distorted, that it can no longer be
recognised as a polygon.
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