How to use the Foucault Device - part 3
It will be difficult to slow down the lateral motion of the knife-edge sufficiently at the moment of its juncture with the axis of the reflected cone of light, so if its motion is arrested as it is about to cut into the rays and gentle downward pressure is applied with the fingers at the right side of the baseboard (Fig. 19), you can probably achieve nice control. If pressing on the baseboard is too lively, apply the pressure to the top of the bench or stand. Always press at the same spot.
In interpreting the shadows which are seen on the mirror, the observer may imagine himself to be in an observation balloon, viewing a small section of the earth's surface (the mirror), which may be a plain, a hill, a crater, or any combination of these contours, as it is being illuminated by the grazing rays of the rising or setting sun (located somewhere to the right of the mirror). In this way a sphere, evenly gray in appearance, would resemble the flat surface of a plain. Even without any exercise of imagination, under the shadow test a sphere does look as flat as the proverbial
pancake. See Fig. 31c, showing knife-edge setting, shadowgraph, and apparent cross-section of a spherical surface.
An oblate spheroid, with its center zone of longer radius, is shown in Fig. 32. The figure is revealed not only by the knife-edge settings, but by the apparent hill that may be seen on the mirror. The slope facing the imaginary sun is illuminated by it, and the opposite slope is in shadow. (The imaginary hill must not, of course, be presumed to cast a shadow, as the source of illumination is only imagined to be at the right.) The surrounding plain is gray, and since the knife-edge is at the center of curvature of that zone, it has the appearance of flatness (Fig. 32, b and c).
It is found that different knife-edge settings will produce different shadow appearances and different apparent cross sections of the same mirror. For example, Fig. 32 shows the shadows and apparent cross sections of an oblate spheroid when the knife-edge is placed at the center of curvature of the center zone a, edge zone b, and an intermediate zone c. It should be noted that, in the case
Fig. 32. Knife-edge shadows on an oblate spheroid.
a. At center of curvature of the center zone.
b. At center of curvature of the edge zone.
c. At center of curvature (not shown) of an intermediate zone.
The shadowgrams represent a typical appearance of an oblate
spheroid seen at each of the respective knife-edge settings. Ap-
parent cross sections of the surface are shown directly below.
Arrows indicate the direction of imaginary rays presumed to cause the lights and shadows.
of the oblate spheroid, apparent elevations represent glass that lies above that reference sphere (shown by the dotted lines) at the center of which the knife-edge happens to be at the moment. By removing the elevations from any of these three figures, a sphere would be obtained, but not, of course, the same sphere in each case. Fig. 33 shows how the shadows appear on a hyperboloidal mirror, wherein the center zone is of a shorter radius than the edge zone. By means of a diagram, the student should show the knife-edge setting that would produce these shadows.
Fig. 33. Shadows on a
hyperboloidal 6-inch f/8
mirror. Dotted lines in the
lower diagrams represent
the reference sphere at the
center of which the knife-
edge is placed.
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