Methods of determining the location of the optimum center of rotation for constant-deviation dispersing prisms such as represented by the Pellin-Broca's prism, as well as for constant-deviation prism systems arranged according to Wadsworth, are described. By rotating the prism or the prism system around this axis, practically no lateral shifting of the central point of either the entrance or the exit aperture of the system occurs, so that the full aperture of the system can be utilized irrespective of the wavelength of light selected by the system.
The optimum center of rotation of the first kind, so may be said, proposed by Forsythe for the Pellin-Borca's prism with 90° deviation angle, and that proposed by Wadsworth for his own mounting, are useful only in a special case when the aperture of the collimator lens or the collector lens is, or both are, definitely smaller than the aperture of the prism. And in almost every case when the apertures of the lenses and the prism have matched dimensions, the optimum center of rotation of the second kind, proposed by the author, affords better utilization of the system.
In the case of the “direct-vision” Wadsworth mounting, the center of rotation of the second kind exists, only when the separation d between the plane of the mirror and the base plane of the prism fulfills the following condition
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where
A is the vertex angle,
b the length of the refracting side plane of the prism, and
i the angle of incidence of the light adopted to determine the “basic configuration” of the system. The centers of rotation of both the first and the second kind coincide in this case.
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