Refractors: Objectives
 
The lens-maker’s formula expresses the focal length, F, of a lens in terms of the refractive index, n, of the material (usually glass) and the radii of curvature, r₁, r₂, of the two lens’ surfaces. It can be expressed conveniently in the form
(1)
(In this form, values of r are positive when light rays meet a convex curvature and are negative when they meet a concave curvature.) Thus, in general, if r₁ is positive and r₂ is negative, a simple lens has a positive, real focus. A beam of parallel light which falls on the lens is, therefore.  By applying this lens to a beam of light from a star which can be considered to be at infinity, an image of the star will be formed at the focus of the lens. This image is available for viewing with an eyepiece or for recording on a detector. The lens acts as light-collector and image-former. When it is used in this way in a telescope system it is commonly known as the objective.

Figure 1. The dispersion curve of a typical crown glass.
 
A single-lens objective is unsatisfactory for astronomical purposes as the images produced suffer from defects or aberrations of different kinds. Considerable effort has been applied to the design of objectives to remove or reduce the aberrations and refractor telescopes show a variety of construction depending on their intended function and the way particular aberrations have been compensated. Telescope objectives may suffer from the following defects:
(i) chromatic aberration,
(ii) spherical aberration,
(iii) coma,
(iv) astigmatism,
(v) curvature of field,
(vi) distortion of field,
and each of these effects is discussed in the following subsections.