Telescope Formulas

Units of measurement are shown but in many cases one can use mm or inches throughout any calculation as long as you are aware the result when a distance value will be in the same units used for the calculation.   A sample 80mm refractor, 10" Dobsonian, and a 11" SCT (Schmidt-Cassegrain) will be used as examples.  The example eyepieces will mostly be a 22mm Televue Panoptic as well as a 9mm TeleVue Nagler eyepiece.  To convert inches to mm we multiply by 25.4.

f ratio (or focal ratio) = primary mirror focal length / primary mirror diameter

Magnification = focal length of primary / focal length of the eyepiece

True field of view = Eyepiece apparent field of view / Magnification  ( AFOV / mag )

Telescope Magnification limit is 40 to 50 times the primary mirror diameter in inches

Eyepiece exit pupil diameter = eyepiece focal length / telescope f ratio

Lowest power useful eyepiece = focal ratio  x  user's eye pupil diameter

Dawes limit =~ 4.56 arc seconds / primary mirror diameter in inches

Handy Sky Distance Measures

Comparison Of Many Optical Systems 

Viewing tools
Magnification of
Light gathering
Max practical
Resolution limit
Resolution limit
Faintest star (visual)

an optimal eyepiece
vs normal eye
magnification
Theory (arc sec)
Practical (arc sec)
(magnitude)
Eyes
1x
1x



5.5
8X50 binoculars
8x
51x
100


10.2
10X50 binoculars
10x
51x
100


10.2
4" telescope f10 20mm eyepc
50x
211x
200
1.1
2.0
11.8
6" telescope f8 16mm eyepc
76x
474x
300
0.8
1.4
12.7
8" telescope f6 12mm eyepc
101x
843x
400
0.6
1.0
13.3
10" telescope f5 10mm eyepc
127x
1317x
500
0.5
0.8
13.8
12" telescope f5 10mm eyepc
152x
1899x
500
0.38
0.7
14.2
15" telescope f5 10mm eyepc
190x
2962x
500
0.3
0.5
14.7
16" telescope f4.5 9mm eyepiece
203x


0.29


18" telescope f4.5 9mm eyepc
228x
4266x
500
0.3
0.5
15.1
20" telescope f5 10mm eyepc
254x
5267x
500
0.2
0.5
15.3
200" 5m hale telescope f3.3
2357x (1)
510204x
500
0.02(2)
0.5(2)
20.3(4)
10m Keck telescope
n/a 2040816x
500
?(2)
?(2)
21.8(4)
2.4m Hubble f10 n/a 117511x
4,700(3)
0.05(3)
0.05(3)
?(4)

(1) The hale telescope is not set up for visual work.  These numbers are my best guess for comparison.

(2) Notice what the atmosphere does to the resolving ability of  large telescopes.  However, these calculations are NOT correct for telescopes such as the Keck.  The Keck uses adaptive optics that partially compensate for atmospheric turbulence.
(3) The Hubble telescope is not degraded at all by the atmosphere.  This is the reason that it is the standard that all other telescopes are compared against.
(4) By using a CCD camera, it is possible to gather light over a long period of time.  This allows fainter stars to be "seen" in pictures than can be seen by the human eye.  Thus, the magnitudes are significantly higher for CCD astronomy than visual astronomy.

Astrospotter.com  thanks www.xmission.com  for the nicely done page from which this page borrows.