## To2ra m2 11 ra

for the position of the exit pupil if the entrance pupil is at the primary. This condition is not the same as (3.380), but the difference is small, the values m2 = -4 and Ra = +0.225 giving 0.961 for the factor in the bracket of (3.381). In an important paper on decentering properties of Cassegrain telescopes, Meinel and Meinel [3.113] point out that the CFP in an RC telescope is close to the exit pupil and attribute the discrepancy to aberrations arising from non-paraxial conditions. While the aberration of the pupil certainly plays a role, the analysis below indicates that the situation is more complex and that the agreement of CFP and ExP depends on the axial obstruction ratio Ha and hence on the final image position. However, the agreement is close in the RC case with normal geometries, as we see from the example above.

It is instructive to analyse further the relation of the pupil position to the position of (CFP)APian from the Schiefspiegler case of Fig. 3.96. We saw that, because the aplanatic telescope has no field coma, there is no effect in rotating the entrance beam about the pole of the primary, the entrance pupil, to produce the situation of Fig. 3.97. If we were to rotate the whole system about the exit pupil, we would have a similar effect. But this is not the same as the CFP, about which only the secondary is rotated, not the primary. Nevertheless, there is a remarkably close coincidence between the two positions CFP and ExP for practical RC telescopes. It is easy to deduce why this is the case. If the bracket terms of (3.380) and (3.381) are equated, we can derive at once the resulting condition for (Ra)p as

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