## The Dawes Limit

Dawes arrived at this relationship in 1867 after tests with a large number of apertures over a number of years. Unfortunately, Dawes only had the experience of refracting telescopes and was not able to comment on the application of this relationship to reflectors, let alone modern catadioptric telescopes! In the next chapter, Christopher Taylor will argue that the Dawes

limit applies equally to reflectors at least to apertures of 30 cm.

Although the Dawes limit is an empirical limit which happens to work well for small apertures (below about 30 cm) it was clear at the turn of the last

Figure 10.2. Image profiles at the Rayleigh limit.

 Table 10.1 Dawes and Rayleigh limits for various apertures Aperture Aperture Dawes Limit Rayleigh Limit (inches) (cm) 1 2.5 4'.'56 5'.'43 3 7.6 1 '.'52 1 '.'82 6 15 0'.'76 0'.'92 8 20 0'.'57 0'.'69 10 25 0'.'46 0'.'55 12 30 0'.'38 0'.'46 16 40 0'.'29 0'.'35 24 60 0'.'19 0'.'23 36 91 0'.'13 0'.'15

Figure 10.3. Image profiles at the Dawes limit.

century, when Aitken and Hussey were using the large American refractors, that it was not a universal limit. In particular it does not apply to unequal pairs and few attempts have been made to try and predict the performance of a given aperture in such cases. In 1914, Thomas Lewis4 produced a number of other relationships between aperture and separating power which, he said, were more relevant to cases where the stars were either unequally bright or both faint.

Christopher Lord has recently attempted5 to produce an empirical law which will predict the resolution of any telescope with any given aperture, central obstruction and seeing, in the case of pairs of any given magnitudes. This has been derived from observations of many binaries with a range of telescopes. For ease of use, a nomogram has been produced.6

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