A telescope's "f/number" is its "focal ratio". A scope with a focal LENGTH of 1000mm and an aperture (diameter) of 100mm has a focal ratio of 10, and is designated "f/10" (divide aperture into focal length). An aperture of 125mm and a focal length of 1000mm would yield f/8.
You will see f/numbers mentioned in telescope advertisements, and you'll read or hear that one telescope is "faster" or "slower" than another. This term and its specification are NOT IMPORTANT VISUALLY. The ancient myth that longer telescopes "see" farther and better just isn't true. All this f/number-stuff means is, the configuration of some scopes will allowastroPHOTOGRAPHY at differing exposure times — it has nothing to do with how bright or how dim images will appear in the eyepiece. For instance, an f/5 telescope is considered "faster", than an f/10 of equal quality, and will produce a photograph of the same object four times faster. If you don't plan on taking astrophotos, then you don't need to be concerned with this term or its specification. The main advantages of a faster telescope are storage and portability, and that's usually why people buy small (short) refractors.
Pictured at left: An example of similar scopes with different f/numbers is Orion's AstroView 120 ST EQ refractor. It's available in both a long and a short version. The long tube is an f/8.3, and the shorty is f/5. They both yield the same quality image in the eyepiece. However, slow (longer focal length) achromatic refractors will exhibit less inherent chromatic aberration than fast ones.
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