Lens construction

The majority type of lenses are spherical lenses, which are fashioned from surfaces that have spherical curvature, that is, the front and back surfaces of the lens can be anticipated to be part of the surface of two spheres of given radii, R1 and R2, which are called the radius of curvature of each surface. The sign of R1 gives the form of the front surface of the lens: if R1 is positive, the surface is convex. If R1 is negative, the front surface is concave. If R1 is infinite, the surface is flat, or has zero curvature, and is said to be plane. The same is true for the back surface of the lens; apart from that the sign conversion is reversed: if R2 is positive, it is concave, and if R2 is negative, the back surface is convex. The line joining the centers of the spheres making up the lens surfaces is called the axis of the lens; in almost all cases the lens axis passes through the physical centre of the lens.

Lenses are divided by the bend of these two surfaces. A lens is biconvex if both surfaces are convex; similarly, a lens with two concave surfaces is biconcave. If one of the surfaces is flat, the lens is termed Plano-convex or Plano-concave depending on the curvature of the other surface. A lens with one convex and one concave side is named convex-concave, and in this case if both curvatures are equal it is a meniscus lens. If the lens is biconvex or Plano-convex, a collimated or parallel beam of light passing along the lens axis and through the lens will be converged to a spot on the axis, at a certain distance behind the lens. In this case, the lens is called a constructive or converging lens.

If the lens is biconcave or Plano-concave, a collimated beam of light passing through the lens is diverged; the lens is thus called a negative or diverging lens. The beam after passing through the lens appears to be emanating from a particular point on the axis in front of the lens; the detachment from this point to the lens is also known as the focal length, although it is negative with respect to the focal length of a converging lens.
If the lens is convex-concave, whether it is converging or diverging depends on the relative curvatures of the two surfaces. If the curvatures are equal, then the beam is neither converged nor diverged.