Formulas
By Matthew Buynoski
FORMULAS
Resolution. The 'theoretical' resolution (in arc-seconds) for a circular aperture is
(1.22 * L * 0.20265)/D where: L is the wavelength of the light involved in nanometers D is the dia. of the aperture in mm.For 203mm diameter, and 600nm light, this works out to 0.73 arc-seconds. There are variations on this formula depending on what one calls "resolution". Another popular variant is to replace the 1.22 by 1.0. In this case, for the same conditions, the resolution is 0.60 arc-seconds.
Magnification is easy: F/f = (tan&)/(tan&) = M
Eyepieces and Field of View...
The exact field-of-view formula:
T = 2 * arctan<(f/F) * tan> where A = apparent field of view T = true field of view F = focal length of the telescope f = focal length of the eyepiece[An approximate formula is T = (f/F) * A where tan & is assumed equal to X]
The eyepieces involved are:
Manufacturer & Model Barrel f A------------------------------------------------------Vixen Lanthanum 1.25" 2.5mm 45 degr.Orion Ultrascopic 1.25" 3.8 52Pentax XL 1.25" 7 65Televue Plossl 1.25" 8 50Televue Nagler 1.25"/2" 9 82Televue Nagler 1.25"/2" 13 82Pentax XL 1.25" 14 65Televue Plossl 1.25" 15 50Orion Plossl 1.25" 17 50Televue Plossl 1.25" 20 50Televue Panoptic 1.25"/2" 22 68Televue Panoptic 2" 27 68Orion Plossl 1.25" 32 50Pentax XL 2" 40 65The magnifications and true fields of view, using the more exact formula, calculate (with F = 2032mm for SCT, 480mm for Ranger) to:
Eyepiece Scope TFOV Magnif. Exit Pupil------------------------------------------------------2.5mm Vixen Ranger 0.25 degr. 192X 0.4mm3.8mm Ultrscpc Ranger 0.44 126X 0.68mm Plossl Ranger 0.89 60X 1.215mm Plossl Ranger 1.67 32X 2.220mm Plossl Ranger 2.22 24X 2.932mm Plossl Ranger 3.56 15X 4.77mm Pentax SCT 0.25 290X 0.79mm Nagler SCT 0.44 226X 0.913mm Nagler SCT 0.64 156X 1.314mm Pentax SCT 0.50 145X 1.417mm Plossl SCT 0.45 119X 1.722mm Panoptic SCT 0.84 92X 2.227mm Panoptic SCT 1.03 75X 2.740mm Pentax SCT 1.44 51X 4.0---------------------------------------------------------The max. AFOV possible for any eyepiece focal length is given by putting in the max. TFOV due to barrel diameter (B) limit:
tan& = B/2F (B is about 31mm for 1.25" eyepieces, and about 50mm for 2" eyepieces)or Tmax = 2 * arctan&so that B/2F = (f/F) * tan&or Amax = 2 * arctan&Tabular form, all entries in degrees... ---Tmax---- ---Amax----F = B=31 B=50 f = B=31 B=50------------------ -------------------480 3.69 5.96 2.5 162* 169*500 3.55 5.72 5 144* 157*750 2.37 3.82 10 114* 136*1000 1.78 2.86 15 91.9* 118*1250 1.42 2.29 20 75.6 103*1500 1.18 1.91 25 63.6 90.6*1750 1.01 1.64 30 54.6 79.62000 0.89 1.43 35 47.8 71.0 *There are no opti-2032 0.87 1.41 40 42.4 64.0 cal designs that can2250 0.79 1.27 45 38.0 58.1 take advantage of2500 0.71 1.15 50 34.4 53.1 these potential large2750 0.65 1.04 55 31.5 48.9 AFOV's.3000 0.59 0.95 60 29.0 45.23250 0.55 0.88 65 26.8 42.13500 0.51 0.82 70 25.0 39.33750 0.47 0.764000 0.44 0.72 Eyepieces come in about 4 flavors on field4250 0.42 0.67 of view: 82 degr. Nagler type, 65-68 degr.4500 0.39 0.64 widefield types, 50 degr. Plossl types, and 40-45 degee ortho types. Compare to the tablevalues to see when a particular type "limits out" for that barrel dia. Forexample, there is no use for f greater than about 25mm on 1.25" barrel widefield eyepieces, or for greater than about 55mm on 2" barrel for a Plossldesign.