Calculations | Data of my Telescopes and Eyepieces | Definitions

On this page, I present some simple formulas for telescopes as well as the resulting data for my telescopes (including the sold ones) and eyepieces. In addition, I provide a few definitions.

 

Calculations

Calculating the Focal Ratio

Focal Ratio (f) = (Focal length of the telescope) / (Diameter of primary mirror)

Examples

Calculating the Magnification (Power)

Magnification = (Focal length of the telescope) / (Focal length of the eyepiece)

Examples

Calculating the Maximum Practical Visual Power (Maximum Usable Magnification)

Maximum Practical Visual Power = (Primary Mirror Diameter) * X = Aperture * X

X amounts to:

Examples

Calculating the Maximum Usable Focal Length of Eyepieces/Minimum Usable Visual Power (Minimum Usable Magnification)

The minimum usable visual power (magnification) is determined by the size of the exit pupil (see below). If the magnification is to low, that is, the exit pupil too large, parts of the light that leaves the eyepiece cannot be utilized by the human eye. This also allows to calculate the minimum usable focal length for eyepieces.

For an exit pupil of 6.5mm, we get the formula: Focal Length of Eyepiece = Focal Ratio * 6.5mm

Examples (Maximum Usable Focal Length of Eyepieces/Minimum Usable Visual Power (Minimum Usable Magnification))

Calculating the Field of View

True field of view = (Apparent field of view) / Magnification = (Apparent field of view) * (Focal length of the eyepiece) / (Focal length of the telescope)

Examples

Sky-Watcher lists 42° as suitable value for most amateur eye pieces.

Measuring the Field of View

The true field of view F of an eyepiece may not always be known and can be determined using a stopwatch (thanks to Jörg Meyer!):

Locate a star of known declination d close to the celestial equator and place it at the eastern edge of the field of view in the eyepiece (motor off!). Measure the time t that the star needs to move through the field of view and enter it into the following equation:

F = (t * 15 * cos d) / 60 (arc minutes)

Calculating the Exit Pupil

Exit pupil = (Diameter of primary mirror) / Magnification = (Focal length of the eyepiece) / (Focal ratio)

Exit pupil = (Diameter of primary mirror) * (Focal length of the eyepiece) / (Focal length of the telescope)

Examples

Depending on your point of view, the exit pupil of an eyepiece can be calculated either from the magnification or the focal ratio of a telescope or a binocular. If the exit pupil of an eye piece is too small, objects become too dim (below 1mm for deep sky objects, below 0.5mm for planets), if it is larger than that of the human eye (>7mm), only part of the light hits the human eye. More on the exit pupil below.

For galaxies, choose an exit pupil of 2-3mm, not at all the maximum magnification (from Internet).

 

Data of my Telescopes and Eyepieces

Visual Power (Magnifation) and other Data for Different Focal Lenghts of Eyepieces

Characteristic Telescope
Further Data
Focal Length of Eyepiece (mm)
   
Focal Length of
Telescope (mm)
5+
6
9
10
12
15
20
25
26++
32
40
Magnification* Heritage P130
650
130.00
108.33
72,22
65.00
54.17
43.33
32.50
26.00
25.00
20.31
16.25
Dobson 10"
1270
254.00
211.67
141.11
127.00
105.83
84.67
63.50
50.80
48.85
39.69
31.75
ETX 90/EC
1250
250.00
208.33
138.89
125.00
104.17
83.33
62.50
50.00
48.08
39.06
31.25
   

Apparent Field
of View (°) >
68
60
52
42?
52
52
52
42?
70
52
42?
Focal Length of
Telescope (mm)
5+
6
9
10
12
15
20
25
26++
32
40
True Field of View (°)** Heritage P130
650
0.52
0.55
0.72
0.65
0.96
1.20
1.60
1.62
2.80
2.56
2.58
Dobson 10"
1270
0.27
0.28
0.37
0.33
0.49
0.61
0.83
0.83
1.43
1.31
1.32
ETX 90/EC
1250
0.27
0.29
0.37
0.34
0.50
0.62
0.84
0.84
1.46
1.33
1.34
   
Diameter of Primary
Mirror (mm)
5+
6
9
10
12
15
20
25
26++
32
40
Exit Pupil (mm) Heritage P130
130
1.00
1.20
1.80
2.00
2.40
3.00
4.00
5.00
5.20
6.40
8.00
Dobson 10"
254
1.00
1.20
1.80
2.00
2.40
3.00
4.00
5.00
5.20
6.40
8.00
ETX 90/EC
90
0.36
0.43
0.65
0.72
0.86
1.08
1.44
1.80
1.87
2.30
2.88

*) Can be doubled wit a 2x Barlow lens
**) The full moon is almost exactly 0.5° in diameter
?) Sky-Watcher lists a field of view of 42° as default value for typical amateur eyepieces (replace by the actual values if known)

+) 5mm: Hyperion wide angle eyepiece (68°) from Baader; it can be used with 1.25" as well as 2" (with 2" also usable with a focal length of 22.5mm).
++) 26mm" Meade QX wide angle eyepiece (70°) for 2" (bought with the Dobson 10")
All other eyepieces are 1.25" eyepieces:

Minimum/Maximum Usable Magnification And Focal Length of Eyepiece

Telescope
Focal Length (mm)
Maximum Usable
Magnification+
Minimum Usable
Magnification*
Maximum Usable Focal
Length of Eyepiece (mm)*
Minimum Usable
Focal Length of Eyepiece (mm)+
Heritage P130
650
195 (1.5); 260 (2)
20
32.5
3.3 (1.5); 2.5 (2)
Dobson 10"
1270
381 (1.5); 500 (2)
39
32.5
3.3 (1.5); 2.5 (2)
ETX 90/EC
1250
180 (2)
13.85
90.3
7 (2)

*) For an exit pupil of 6.5mm
+) Factor 1.5 or 2 for Dobson telescopes; Teleskop-Service uses the lower value of 1,5 for Newtonian telescopes in general

Use of Magnifications

 

Definitions

Eye Relief

Short: Eye relief is defined as the distance a binocular or spotting scope can be held away from the eye and still presents the full field of view. (From deu.proz.com/kudoz/english_to_german/physics/2699015-eye_relief.html)

Wikipedia: The eye relief of a telescope, a microscope, or binoculars is the distance from the last surface of an eyepiece at which the eye can be placed to match the eyepiece exit pupil to the eye's entrance pupil. Short eye relief requires the observer to press his or her eye close to the eyepiece in order to see an unvignetted image. An exit pupil larger than the observer's pupil wastes some light, but allows for movement between eye and eyepiece without vignetting. Conversely, an exit pupil smaller than the eye's pupil results in a vignetted image. The optical designer must also consider that the pupil of the human eye varies in size with lighting conditions and the age of the observer.

Eye relief can be particularly important for eyeglass wearers and shooters. The eye of an eyeglass wearer is typically further from the eye piece which necessitates a longer eye relief in order to still see the entire field of view. (From Wikipedia)

Exit Pupil

In optics, the exit pupil is a virtual aperture in an optical system. Only rays which pass through this virtual aperture can exit the system. The exit pupil is the image of the aperture stop in the optics that follow it. In a telescope or compound microscope, this image is the image of the objective element(s) as produced by the eyepiece. The size and shape of this disc is crucial to the instrument's performance, because the observer's eye can see light only if it passes through this tiny aperture.

To use an optical instrument, the entrance pupil of the viewer's eye must be aligned with and be of similar size to the instrument's exit pupil. This properly couples the optical system to the eye and avoids vignetting. (The entrance pupil of the eye is the image of the anatomical pupil as seen through the cornea.) The location of the exit pupil thus determines the eye relief of an eyepiece. Good eyepiece designs produce an exit pupil of diameter approximating the eye's apparent pupil diameter, and located about 20 mm away from the last surface of the eyepiece for the viewer's comfort. If the disc is much larger than the eye's pupil, much of the light will be lost instead of entering the eye; if smaller, the view will be vignetted. If the disc is too close to the last surface of the eyepiece, the eye will have to be uncomfortably close for viewing; if too far away, the observer will have difficulty maintaining the eye's alignment with the disc.

For a telescope, the diameter of the exit pupil can be calculated by dividing the focal length of the eyepiece by the focal ratio (f-number) of the telescope. More simply, it is the diameter of the objective lens divided by the magnification (see calculations above).

The exit pupil determines in the direction of the eye the minimum as well as the maximum usable magnification of an optical instrument. (From Wikipedia)

After dark adaptation, the pupil is about 7mm wide for young people and about 6.4mm wide for adults; it gets smaller with growing age. An exit puil of 4mm is suitable and sufficient for observers of all ages. If the exit pupil of an eyepiece is larger than the observer's pupil, light is wasted that falls outside of the human pupil. If the exit pupil of an eye piece is too small, objects become too dim (below 1mm for deep sky objects, below 0.7mm for planets, below 0.5mm for the moon)

 

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04.05.2010