The Paraboloid
As mentioned in the first chapter, the mirror must have a paraboloidal figure in order that all rays entering the telescope parallel to its axis will converge to meet in a single point in the focal plane (Fig. 10b). It was also stated that a spherical mirror might be altered into that figure in any one of three ways. But not...
Fig. 34.
To obtain the conic sections shown at the right, a cone is cut by planes as drawn at the left: parallel to the base for a circle, C; parallel to a side for a parabola, P; between these for an ellipse, E; in a plane steeper than the parabola for a hyperbola. Rotation of a circle around any axis produces a spheroidal (spherical) surface.
Rotation of the parabola and hyperbola about their respective axes produces surfaces of revolution called paraboloid and hyperboloid. Rotation of the ellipse about its major axis produces an ellipsoid; about its minor axis, an oblate spheroid.
.....the same size of paraboloid would be derived in each case, although, like spheres, the shapes of all paraboloids are the same. The dotted curves in Fig. 35 represent the paraboloidal surfaces that could be obtained from the same spherical mirror by the three methods. At a, the bulk of glass is removed from the central zones, tapering down to zero at the edges. The paraboloid thus obtained has a slightly shorter focal length than the original spherical
the paraboloid part 2 |
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