Simple Convex and Concave
Convex and concave telescope lens are the most basic styles of lenses and consist of a single lens, or piece of glass with either both sides curving inward (concave) or curving outward (convex). These lenses are the most rudimentary. A convex lens when used to view objects will turn the image upside down because of the refraction through the lens. A concave lens will not turn an object upside down but the depth of the curve of a concave lens will determine its strength. A deeper curve, in a concave lens will produce a clearer image.
Meniscus
A meniscus lens is a common telescope lens that is also in many other items that require lenses, such as glasses. A meniscus lens has a concave side and a convex side. The combination of the two curvatures allows a quality focus and allows the image to appear right side up.
Doublet and Triplet
The combination of lenses in a telescope -- whether convex, concave or meniscus -- forms a doublet or triplet. A doublet is the combination of two lenses and the combination of three is a triplet. These combinations allow varied focused. The varied arrangements of lenses are a result of the distance between each lens and the order of their placement. Doublets and triplets are most often in the eyepiece of the telescope rather than its main tube.
Eyepieces
Eyepieces of telescopes also contain lenses and tend to contain combinations, or triplets and doublets. Five types of are typical in eyepiece lenses. Each type has had its popular periods but improvements and new lens designs have pushed some aside. The lenses provide users wide view, clear focus, good colors and little eye strain. The most popular include the Plossl telescope eyepiece, Orthoscopic telescope eyepiece, and the Erfle telescope eyepiece.
Reflecting Telescopes
All of the examples of lenses so far are examples of refracting telescopes. The combination of a mirror and a lens or lenses is a reflecting telescope. A reflecting telescope, rather than gathering light with the lenses, uses the body or tube of the telescope and then bounces the light off the mirror to the lens.