Telescope Optics Explorer

Three modes: single telescope analysis with an optical ray diagram, side-by-side comparison of two telescopes, and an eyepiece finder that shows results for seven standard eyepiece focal lengths. Six presets from 10×50 binoculars to the Hubble Space Telescope.

Mode

Presets

200 mm
30500 mm
1200 mm
1005000 mm
25 mm
250 mm
550 nm
380 nm750 nm

Optical Diagram

D = 200 mmf = 1200 mmf/6.025 mmEP48.0×

Optical Properties

200 mm | f/6.0 | 25 mm EP
48.0×
200 mm aperture, 1200 mm focal length
Rayleigh Resolution
0.69 ″
Dawes Limit
0.58 ″
Magnification
48.0×
Focal Ratio
f/6.0
True FOV
1.04°
Exit Pupil
4.17 mm
Limiting Magnitude
13.5 mag
Light Gathering
816×
Max Useful Mag
400×
Min Useful Mag
28.6×
Resolution
0.69″
Light Gathering
816×
Limiting Mag
13.5
Max Mag
400×

Reference Guide

Resolution and Dawes Limit

The Rayleigh criterion gives the smallest angle a telescope can resolve, set by diffraction at the aperture.

θ=1.22λD\theta = 1.22\,\frac{\lambda}{D}

In arcseconds, multiply by 206 265. For visible light (550 nm) through a 200 mm aperture, resolution is about 0.69″.

The Dawes limit is an empirical formula for resolving equal-brightness double stars.

θDawes=116D(mm)\theta_{\text{Dawes}} = \frac{116}{D\,(\text{mm})}

Magnification and Field of View

Magnification equals the objective focal length divided by the eyepiece focal length.

M=fobjfeyeM = \frac{f_{\text{obj}}}{f_{\text{eye}}}

The true field of view (TFOV) seen through the eyepiece equals the apparent field (AFOV, typically 50°) divided by magnification. Higher magnification gives a narrower view.

TFOV=AFOVM\text{TFOV} = \frac{\text{AFOV}}{M}

Maximum useful magnification is roughly 2× the aperture in mm. Above that, you magnify atmospheric blur more than detail. Minimum useful is D/7, where the exit pupil equals the eye's dark-adapted pupil (7 mm).

Light Gathering and Limiting Magnitude

A telescope collects light in proportion to the area of its aperture compared to the dark-adapted eye (7 mm pupil).

LGP=(DDeye)2\text{LGP} = \left(\frac{D}{D_{\text{eye}}}\right)^2

A 200 mm telescope gathers about 816 times more light than the naked eye, allowing you to see objects roughly 7.3 magnitudes fainter.

mlim=2+5log10(Dmm)m_{\text{lim}} = 2 + 5\,\log_{10}(D_{\text{mm}})

The limiting magnitude formula estimates the faintest star visible through the scope under ideal conditions.

Choosing Eyepieces

The exit pupil is the diameter of the light cone leaving the eyepiece and entering your eye.

EP=DM\text{EP} = \frac{D}{M}

If the exit pupil exceeds 7 mm (dark-adapted pupil), light is wasted. If it falls below about 1 mm, the image becomes uncomfortably dim and eye floaters become visible.

Eyepiece useTypical focal length
Wide-field / sweeping 32 - 40 mm
General observing 17 - 25 mm
Planetary detail 8 - 12 mm
High-power doubles 4 - 6 mm