Telescope & Optics Calculator
Compute magnification, resolving power, field of view, and optimal eyepiece combinations for your telescope.
Telescope Parameters
Light Pollution (Bortle Scale)
Understanding Telescope Optics
Aperture — the diameter of a telescope's primary mirror or lens — is the single most important specification. A larger aperture gathers more light (proportional to area, i.e., the square of the diameter), revealing fainter objects and resolving finer detail.
Magnification is simply the telescope focal length divided by the eyepiece focal length. While higher magnifications can be computed, usable magnification is limited by aperture: the theoretical maximum is roughly 2× the aperture in mm (e.g., 400× for a 200 mm scope). Beyond this, the image becomes dim and blurry due to diffraction.
For deep-sky observing, lower magnifications (larger exit pupils) are preferred to maintain surface brightness. For planets and the Moon, higher magnifications help reveal detail as long as atmospheric seeing permits.
The exit pupil is the diameter of the cone of light leaving the eyepiece, calculated as aperture ÷ magnification (or equivalently, eyepiece FL ÷ focal ratio). It represents the bright disk you see when you hold the eyepiece at arm's length.
The dark-adapted human pupil dilates to roughly 6–7 mm (less with age). If the exit pupil exceeds your pupil diameter, some of the gathered light is wasted — it falls on your iris rather than your retina.
For deep-sky viewing, an exit pupil of 4–7 mm maximises surface brightness. For planetary detail, 1–2 mm exit pupils are typical. Full dark adaptation takes 20–30 minutes and is easily disrupted by bright light — use a red torch to preserve it.
The ability of a telescope to separate two closely spaced objects is called its resolving power, limited by diffraction.
Dawes Limit: An empirical formula determined by William Dawes for equal-brightness double stars: θ = 116 / D (arcseconds, D in mm). This represents the closest separation at which two stars can just be distinguished.
Rayleigh Criterion: A more rigorous diffraction limit: θ = 138 / D (arcseconds, D in mm, for 550 nm light). At this separation, the central maximum of one star's Airy disk falls on the first minimum of the other.
In practice, atmospheric seeing (typically 1–3 arcseconds) often limits resolution more than the optics, especially for larger apertures.
The Bortle Dark-Sky Scale, introduced by John Bortle in 2001, rates the night sky darkness from Class 1 (the darkest skies on Earth — zodiacal light visible, limiting magnitude ~7.6+) to Class 9 (inner-city skies — only the Moon, planets, and a few bright stars visible, limiting magnitude ~4.0).
| Class | Description | NELM |
|---|---|---|
| 1 | Excellent dark-sky site | 7.6–8.0 |
| 2 | Typical truly dark site | 7.1–7.5 |
| 3 | Rural sky | 6.6–7.0 |
| 4 | Rural/suburban transition | 6.1–6.5 |
| 5 | Suburban sky | 5.6–6.0 |
| 6 | Bright suburban sky | 5.1–5.5 |
| 7 | Suburban/urban transition | 4.6–5.0 |
| 8 | City sky | 4.1–4.5 |
| 9 | Inner-city sky | 4.0 or less |
Unlike stars (point sources), nebulae and galaxies are extended objects whose light is spread over an area. While a larger aperture gathers more total light, magnification spreads it over a larger retinal area, reducing surface brightness.
The surface brightness of an extended object through a telescope never exceeds its naked-eye surface brightness — it can only be equal (at minimum magnification, exit pupil = eye pupil) or lower. This is why large, faint nebulae often look best at low magnification with a wide-field eyepiece.
Narrowband filters (O-III, H-beta, UHC) can dramatically improve contrast by blocking light pollution and passing only the emission wavelengths of the nebula.