Telescope Optics Formulas with Calculators
List of Calculators 

1. Focal Ratio 2. Focal Length 
4. Dawes Limit 
Hi, Ray Shore here. This page is dedicated to formulas related to telescope optics. I have listed the main formulas below for these calculations; each with a handy calculator. To the right, I have listed the specifications for my SchmidtCassegrain optical tube. The examples below will reference these specs. 
Specifications for My C8 Optical Tube:

Focal Length/Aperture
The smaller the fratio, the faster the telescope. Fast telescopes (e.g. f/4 or f/6) provide wider fields of view (FOV) making them most suitable for deep space observation.The larger the fratio, the slower the telescope. The FOV becomes smaller as the fratio gets larger. Telescopes with large fratio's (e.g. f/8 or f/10) are most suitable for high power planetary work.
Example: my telescope has a large fratio (f/10). To calculate, I take the focal length of 2032mm and divide by it's aperture of 203.2mm. The result is f/10. My scope is well suited for high planetary observation and imaging.

Important note: the focal length and aperture should be in the same units for this calculation. In my example above, I converted my 8" aperture to 203.2mm because the focal length was in mm. 
Aperture X Focal Ratio
Description: length of the light path from the lens or mirror to the focus point.
Example: I take my aperture of 203.2mm and multiply by my fratio of f/10. The result is 2032mm.

Note: some people prefer that their focal length be stated in inches rather than millimeters. 
Telescope Focal Length / Eyepiece Focal Length
Example: If I'm using a 25mm eyepiece with my scope, I take my scope focal length of 2032mm and divide by 25mm and I get 81X of magnification.
A general rule of thumb for applying power is no more than 50X of magnification per inch of aperture.
Example: the aperture of my scope is 8". Taking that times 50 gives me a limit of about 450X. Generally I don't come close to using that much power!

Solar System Software Tools

4.56 arc seconds/ objective diameter in inches
Pertains to the resolving power of an optical system (generally referred to when splitting double stars). The higher the resolving power, the smaller the minimum visible detail or minimum angle of resolution. The lower the resolving power, the bigger the minimum visible detail or minimum angle of resolution.
Example: taking 4.56 arc seconds and dividing by my scopes objective diameter of 8" gives me 0.57 arc/sec of resolving power. This means that I could theoretically split a double star with 0.57 arc/seconds of separation.

Click here to convert from millimeters to inches


Apparent Field of Eyepiece / Magnification
This is important if you want to know the size of the object that can be observed. The apparent field of an eyepiece should be supplied by the eyepiece manufacturer.
Example: if I'm using a 10mm eyepiece with an apparent field of view of 46 degrees then I divide 46 by 203.2 (power derived from 2032/10). This gives me a true field of view of 0.2 degrees.
