Focal Length and Focal Ratio
The optical length of a telescope can be expressed in two ways: As the focal length - the length of the light path to the focal plane in millimeters or as the Focal Ratio - ratio of the focal length divide by the aperture in millimeters.
The focal length of a telescope is important because that is used to calculate the power or magnification that a given eyepiece will have with a given telescope. Eyepieces have focal lengths also (typically between 4-50mm). To calculate power you divide the focal length of the telescope by the focal length of the eyepiece.
Also known as “F/Stop” or “Photographic Speed”, the focal ratio is the relationship between the focal length and the aperture. A 10-inch scope with the focal length of 100 inches would have the focal ratio of 10. This would be expressed as f/10 or f10.
Just like with cameras, the lower the focal ratio the faster (brighter) the optical system. Lower focal ratios have gentler curve to their optical elements and produce less optical aberrations.
Frequently, there is a false impression that the surface brightness of an astronomical object is determined by the focal ratio of the telescope. In reality, the surface brightness is determined by the light grasp of a telescope, which is a function of the area of the aperture of the telescope.