The formulas
M = Feyepiece ÷ Fobjective
Tube length (cm) = 100 ÷ Fobjective + 100 ÷ Feyepiece
- F
- Lens powers in dioptres. The eyepiece is minus in a Galilean telescope and plus in a Keplerian one; the calculator sets the sign from the type.
- M
- Angular magnification, shown without its sign.
Galilean or Keplerian
| Objective | Eyepiece | Type | Magnification | Tube length |
|---|---|---|---|---|
| +10 D | −20 D | Galilean | 2.0x | 5.0 cm |
| +10 D | +20 D | Keplerian | 2.0x | 15.0 cm |
| +10 D | −40 D | Galilean | 4.0x | 7.5 cm |
| +10 D | +40 D | Keplerian | 4.0x | 12.5 cm |
| +8 D | −20 D | Galilean | 2.5x | 7.5 cm |
At the same magnification the Keplerian tube is three times longer at 2x. It also needs prisms to turn the image upright, which adds weight, but its exit pupil sits behind the eyepiece where the eye can reach it, so its field is wider.
Field of view
The calculator gives the magnification; the field follows from it. Roughly, the true field is the apparent field of the eyepiece divided by the magnification: an eyepiece with a 40° apparent field in a 4x telescope shows about 10°. A Galilean telescope's field also depends on the objective diameter and how close the eye is to the eyepiece, so use the maker's figure where there is one.
Magnification needed is current acuity divided by the acuity wanted. To bring 20/100 to 20/40 takes 100 ÷ 40 = 2.5x, which the +8 D / −20 D Galilean in the table gives.
Limits
- Thin lenses focused for distance. Reading caps and focusing for near are not included.
- Field of view is worked by hand as above; the calculator does not compute it.
- See the medical disclaimer.
Questions
Why are most spectacle-mounted telescopes Galilean?
They are shorter and lighter and give an upright image without prisms. The price is a narrower field of view than a Keplerian telescope of the same magnification.
Can a distance telescope be used for reading?
Yes, with a reading cap: a plus lens over the objective focuses the telescope at the cap's focal length, 25 cm for a +4.00 D cap (100 ÷ 4). The total magnification is the telescope's multiplied by the cap's, taken as cap power ÷ 4.