L

where L = M2I2 in Figs. 2.11 and 2.12. In terms of ray trace parameters L = s2. Note that Eq. (2.57) is only valid if |L| > |d1|, i.e. if b > 0, since otherwise the true length of the system is given by |d1|, not |L|.

Another fundamental parameter of these compound telescope forms is the axial obstruction ratio Ra. This is given by

yi / f from the geometry of Figs. 2.11 and 2.12. Eqs. (2.57) and (2.58) give the simple relationship

This result essentially explains why the compound (2-mirror) telescope has triumphed over the single mirror form and is the standard solution for modern astronomy. Historically it was desirable to have a large scale (see ยง 2.2.6 below) and therefore a long focal length f . A solution with a large T giving reduced length is exactly what is needed. The fact that a large value of T gives a small axial obstruction from (2.59) is a marvellous added attraction. Of course, we have said nothing about the difficulties of manufacture and test which, as we shall see in Chap. 5 and in RTO II, Chap. 1 and 3, have been formidable.

Formally, from (2.57) and (2.59), there is no difference between the Gregory and Cassegrain solutions. However, there is a further parameter to be introduced which makes the Cassegrain solution much superior for normal purposes, i.e. where a real primary image is of no consequence. The notable exception is the Gregory form for solar telescopes, in which the intense heat of the bulk of the solar image can be absorbed at the real prime focus. The parameter favouring the Cassegrain form is the position of the final image I2. For a fixed, convenient position behind the primary and a given value of

Ra, the Cassegrain allows a larger relative aperture u2 or a shorter value of / because L is shorter. This is evident from Figs. 2.11 and 2.12 but will be proven by the formulae below.

Applying (2.34) and (2.35) to the secondary, we have

giving with L = s2

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