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Telescope Optics Formulas with Calculators

Telescope Optics Formulas with Calculators

 

List of Calculators

1.   Focal Ratio

2.   Focal Length    

3.   Magnification

4.   Dawes Limit

5.   True Field of View

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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 Schmidt-Cassegrain optical tube. The examples below will reference these specs.

    Specifications for My C8 Optical Tube:

  • Aperture: 8" (203.2 mm)

  • Focal Ratio: f/10

  • Focal Length: 2032 mm

  • Highest Useful Magnification: 450X

  • Resolution: .57 arc/sec


    1. Focal Ratio

    Focal Length/Aperture

    The smaller the f-ratio, 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 f-ratio, the slower the telescope. The FOV becomes smaller as the f-ratio gets larger. Telescopes with large f-ratio's (e.g. f/8 or f/10) are most suitable for high power planetary work.

    Example: my telescope has a large f-ratio (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.

    Focal Ratio Calculator

    Focal Length:

    aperture:



    f-Ratio Result:


    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.

    Click here to convert units

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    2. Focal Length

    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 f-ratio of f/10. The result is 2032mm.

    Focal Length Calculator

    Focal Ratio: f/

    aperture (mm):



    Focal Length Result:

    Note: some people prefer that their focal length be stated in inches rather than millimeters.

    Click here to convert  to inches

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    3. Magnification

    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!

    Magnification Calculator

    Scope Focal Length (mm):

    Eypiece Focal Length (mm):



    Magnification Result:

    Click here to convert from inches to millimeters.

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    4. Dawes Limit

    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.

    Dawes Limit Calculator

    Scope Diameter (Inches):



    Resolving Power:

     

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    Click here to convert from millimeters to inches

     

     

     

     

     

     


    5. True Field of View

    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.

    True FOV Calculator

    Apparent Field of Eyepiece (degrees):

    Magnification (X):





    FOV (Degrees):

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