I too was intrigued by the mention of Cains’ magic number but could not find an online reference to the eponymous magic number. However, I remember reading somewhere that although the dynamic range of exit pupil is ~1-7 mm, an exit pupil of 2-3 mm is considered optimal for maximizing resolving power. Since
exit pupil (mm) = aperture (mm)/magnification, and
PPI (power/inch) = magnification/aperture (inch) = 25.4 x magnification/aperture (mm) = 25.4/exit pupil (mm),
substituting an exit pupil of 2-3 mm, we find that the optimal PPI is 8.5-12.7 power/inch, which the upper limit is close to Cains’ magic number of ~13, probably where the number comes from.
I find the following websites helpful in determining useful ranges of PPI for visual observing:
http://www.chuckhawks.com/ocular_starter_set.htmhttp://www.cloudynights.com/page/articles/cat/articles/how-to/useful-magnification-ranges-for-visual-observimg-r535These are summarized below:
- Low magnification: 3.7-9.9 power/inch (David Knisely), 5-8 power/inch (Chuck Hawks)
- Medium magnification: 10-18.9 power/inch (David Knisely), ~10 power/inch (Chuck Hawks)
- Medium-high magnification: 15-20 power/inch (Chuck Hawks)
- High magnification: 19-31.9 power/inch (David Knisely), ~30 power/inch (Chuck Hawks)
- Very high magnification: 32-46.9 power/inch (David Knisely)
- Extreme magnification: 47-75 power/inch (David Knisely), although most people would argue that magnification >50 power/inch is empty magnification.
Therefore, Cains’ magic number of ~13 power/inch would fall within Medium Magnification range. From my own experience, I generally prefer PPI of ~10 power/inch, which is more in line with Chuck Hawks’ recommendation. To determine which eyepiece to use for given exit pupil or PPI and f-ratio,
eyepiece (mm) = exit pupil (mm) x f-ratio = 25.4 x f-ratio / PPI
Hope this helps with finding your optimal eyepiece for your telescope.