How to use the Foucault Device - part 2
As zonal measurements are not going to be made at this stage, the knife-edge block need not bear against the guide cleat during these preliminary tests. The separation of the pinhole and knife-edge should not be great, however.
Theory tells us that if they are at unequal distances from the mirror, an error is introduced in the correction formula for the paraboloid, and if they are widely separated laterally, astigmatism is introduced. But within a range of a few inches either way no measurable error can be observed. Now push the knife-edge across laterally until it cuts into the rays and causes a shadow to be cast on the mirror. Let us imagine that it is in the position shown in Fig. 31a. Here, it is inside the center of curvature, and the first rays to be cut off are those coming from the left edge of the mirror, so this part of it will darken first,
Fig. 31. Knife-edge shadows on a spherical mirror.
a. Inside center of curvature. The shadow moves in from the
left, in the same direction as the knife-edge movement.
b. Outside of center of curvature. The shadow comes in from
the right, in a direction opposite to the movement of the
knife-edge.
c. At center of curvature.
The shadow fills the entire mirror evenly and instantly.
the shadow advancing across the mirror from left to right, in the same direction as the knife-edge is moving. Now draw the knife-edge back about I/2" toward the eye, to the position of Fig. 31b. Here, it is beyond the center of curvature, and the first rays to be intercepted come from the right-hand side of the mirror, so the shadow starts there and advances from right to left, in a direction opposite to that of the knife-edge movement. We have now "bracketed the target," as artillerymen say, and the center of curvature is somewhere between these two settings.
It is finally found by repeated trials, and if the mirror is truly spherical it will darken evenly and instantly the moment the knife-edge has cut completely across the pinhole image, and no direction of shadow approach can be detected. Even with an unduly large
pinhole, this condition would still be true. A spherical surface will hardly be found at this stage, however, and instead of all of the reflected rays intersecting at c, there will probably be a scattering of intersecting zonal rays along a short section of the axis of the cone, as in Figs. 21b and 32, or possibly as in Fig. 39.
In these cases, as the knife-edge is cut in, some parts of the mirror will remain illuminated while other parts are in shadow. With a very large pinhole, slight zonal discrepancies, distinguishable only by a faint contrast in shading, might not be apparent in the broad transition from light to shadow, and for this reason a large pinhole is less sensitive than a small one.
part 3 how to use the Foucault Device |
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