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Formulas for Telescopes and Telescope Making

 

Without getting too technical I have compiled a set of different formulae for telescopes. They range in scope from forumulae that are useful for making telescopes to forumulae that are useful in understanding and using telescopes. If you know of a formula that would be a good addition to this page be sure to send me an email!

The Magnification of a telescope:

M = f / fe

Or the Magnification (M) = The focal length of the objective (f) divided by the focal length of the eyepiece (fe)

The Exit pupil size of a telescopes optics:

h = a / m

Or the Exit pupil size (h) = the objective diameter divided by the magnification

Minimum and maximum magnification

Minimum magnification = 3.62 X the aperture of the telescope in inches Anything more than this would cause an exit pupil that is too large on the telescope so there would be waste because your eye can't take it all in.

Maximum magnification. Is much more complex to calculate and the quality and type of the optics is critical. Typically a good rule of thumb is a magnification of about 50X to 60X per inch of aperture.

Diagonal Mirror Placement when building a newtonian reflector:

Key:
r = Mirror radius in inches
f = focal length of primary mirror
h = distance of desired location of focal plane from the optical axis
m = the ideal minor axis dimension of the diagonal mirror
d = amount of necessary offset in inches

to find m: m = 2rh/f + (fh)/60
to find d: d= 0.7 mr/f

Limiting Magnitudes of Telescopes

This is a formula that gives you the approximate lowest magnitude star (faintest) that a telescope can see based on it's aperture

m = magnitude

m ~ 8.8 +5log a where a is inches

Note that there is an excellent online calculator that has a series of variables that you can plug in including the type and size of telescope, cleanliness of the objective and even your age! Online Limiting Magnitude calculator

Just for reference I have created some general numbers using that calculator based on a newtonian telescope and everything else about average and a magnification of 100X.

Aperture of telescope Faintest star magnitude
4 13
6 13.7
8 14.1
10 14.4
12 14.7

 

 

 

 

 

 

 

 

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