S 2

giving

The image position is defined by the parameter b, where b = L + /1 - S2 = L + /1 (1 - Ra) , (2.65)

The relative aperture of the emergent beam is defined by u2 from Figs. 2.11 and 2.12 as 2

from (2.58). Eq. (2.66) is the relationship which proves the advantage of the Cassegrain form over the Gregorian. If y1 and Ra are predefined, then the angle u2 depends only on L. Now L is given for a predefined image position b from (2.65) as

in which /1 is negative in both cases and Ra is, from (2.58), positive in the Cassegrain form and negative in the Gregory form. Since L is a positive quantity in both cases, it is always larger in the Gregory form for a given Ra. Therefore, u2 must be smaller for the Gregory form from (2.66) unless |Ra| is zero, a limit case of no practical significance. Typically |Ra| = 3 .If b = 0, Eq. (2.67) shows that L is twice as large for the Gregory form. T is the same in both cases, so |/ | is twice as large for the Gregory form from

(2.57). From (2.55) m2 is also twice as large, making the solution technically more extreme and sensitive. But, above all, the "speed" of the telescope in the photographic sense is reduced to a quarter by the halving of u2 in (2.66). In other words, the Light Transmission Power defined in Eq. (2.47) is much higher in the Cassegrain case for given values of Ra , T, y1 and b. Combining (2.66) and (2.67) gives

In § 2.2.4 we introduced the basic parameter C, the compression ratio, for an afocal telescope, defined from (2.48) by

If either the Gregory or Cassegrain form is made afocal, it becomes a Mersenne telescope as discussed in Chap. 1 (see Fig. 1.3). In this case

from (2.58). As in the refracting case, the Lagrange Invariant of (2.50) also gives

where m is the magnification of the total afocal system.

We return now to the normal case with a real image. So far, the parameter d1 has hardly appeared in our paraxial relationships. It is nevertheless an important parameter, defined by

y1 f m/ /1 /1 f relations of great importance in the aberration theory of Chap. 3. Further useful relations are

/2S2 S2 - /2 from (2.61), and d1 = b - s2 = b - L (2.74) 