An important limit case remains to be considered. If, in Eq. (2.84), m2 becomes either +1 or -1, the denominator becomes zero. The case m2 = + 1 corresponds to a real limit case of the Gregory telescope in which the secondary has its centre of curvature at the primary image in Fig. 2.11. The final image is then returned to and P = 0, so that f2 is indeterminate from (2.84). In fact, it would be equal to s2/2. The case is of no practical interest since it represents an autocollimator returning the incident parallel beam into space.
The case m2 = -1, on the other hand, has considerable practical interest as the limit case of a Cassegrain telescope in which the secondary has zero power and becomes a plane mirror (Fig. 2.15). Since P is real and positive, the numerator of (2.84) remains finite and f2 = ro. For this limit case, we can write, using ~ to denote the plane mirror solution, f = -A , (2.97) and from (2.58)
L = -Rf , (2.98) giving correctly f2 = ro from (2.64). Now, from (2.65)
Eliminating L from (2.98) and (2.99) gives
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