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&

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 &

The eyepieces involved are:

Manufacturer & Model Barrel f A ------------------------------------------------------ Vixen Lanthanum 1.25" 2.5mm 45 degr. Orion Ultrascopic 1.25" 3.8 52 Pentax XL 1.25" 7 65 Televue Plossl 1.25" 8 50 Televue Nagler 1.25"/2" 9 82 Televue Nagler 1.25"/2" 13 82 Pentax XL 1.25" 14 65 Televue Plossl 1.25" 15 50 Orion Plossl 1.25" 17 50 Televue Plossl 1.25" 20 50 Televue Panoptic 1.25"/2" 22 68 Televue Panoptic 2" 27 68 Orion Plossl 1.25" 32 50 Pentax XL 2" 40 65

The 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 0.4mm 3.8mm Ultrscpc Ranger 0.44 126X 0.6 8mm Plossl Ranger 0.89 60X 1.2 15mm Plossl Ranger 1.67 32X 2.2 20mm Plossl Ranger 2.22 24X 2.9 32mm Plossl Ranger 3.56 15X 4.7 7mm Pentax SCT 0.25 290X 0.7 9mm Nagler SCT 0.44 226X 0.9 13mm Nagler SCT 0.64 156X 1.3 14mm Pentax SCT 0.50 145X 1.4 17mm Plossl SCT 0.45 119X 1.7 22mm Panoptic SCT 0.84 92X 2.2 27mm Panoptic SCT 1.03 75X 2.7 40mm 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 79.6 2000 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 can 2250 0.79 1.27 45 38.0 58.1 take advantage of 2500 0.71 1.15 50 34.4 53.1 these potential large 2750 0.65 1.04 55 31.5 48.9 AFOV's. 3000 0.59 0.95 60 29.0 45.2 3250 0.55 0.88 65 26.8 42.1 3500 0.51 0.82 70 25.0 39.3 3750 0.47 0.76 4000 0.44 0.72 Eyepieces come in about 4 flavors on field 4250 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 table values to see when a particular type "limits out" for that barrel dia. For example, there is no use for f greater than about 25mm on 1.25" barrel wide field eyepieces, or for greater than about 55mm on 2" barrel for a Plossl design.