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What Does the Radius of Curvature of a Telescope Lens Affect?

The basic optical system of a telescope consists of a large lens that gathers light and an eyepiece lens that magnifies the resulting image. Both lenses have a radius of curvature for the front surface and for the back surface of each lens, and these radii of curvature determine the focal lengths of the lenses. The magnification of the telescope is in turn determined by the ratio of focal lengths of the two lenses.

Definition of Radius of Curvature of a Lens
- A radius of curvature is the radius of a circle that passes through the points on the surface of a lens. The two lenses of a telescope optical system are usually convex. They will have two surfaces so one side has a positive radius of curvature while the other side will be curved in the opposite direction and will have a negative radius of curvature. The four radii of curvature help determine the basic characteristics of the telescope.
Effect of Radius of Curvature on Focal Length
- The focal length of a lens is given by the formula 1/F = (n-1)(1/c1 - 1/c2) where F is the focal length of the lens, n is the refractive index of the lens material, c1 is the radius of curvature of the front of the lens and c2 is the radius of curvature of the back of the lens. It is clear from the formula that increasing the radius of curvature will increase the focal length of the lens.
Focal Length and Magnification
- The magnification of a telescope is determined by the focal lengths of the two lenses. It is given by the ratio F1/F2, where F1 is the focal length of the main lens and F2 is the focal length of the eyepiece lens. To get a high magnification for a telescope, the focal length of the main lens should be large and the focal length of the eyepiece lens should be small. Typical values for a small telescope would be a focal length of 24 inches for the main lens and 0.5 inches for the eyepiece, giving a magnification of 48 times.
Radius of Curvature and Telescope Design
- An ideal telescope will produce a large, bright image. While there will always be other limiting factors such as cost and space concerns, basic optical design suggests that a large lens with a large radius of curvature giving a long focal length is the best choice for the main lens. For the eyepiece, a lens with a small radius of curvature giving a small focal lens will be the most effective. The radius of curvature of each lens is therefore one of the basic parameters determining the performance of the telescope.

Astronomy