Construction of simple lenses

Most lenses are spherical lenses: their two surfaces are parts of the surfaces of spheres. Each surface can be convex(bulging outwards from the lens), concave (depressed into the lens), or planar (flat). The line joining the centres of the spheres making up the lens surfaces is called the axis of the lens. Typically the lens axis passes through the physical centre of the lens, because of the way they are manufactured. Lenses may be cut or ground after manufacturing to give them a different shape or size. The lens axis may then not pass through the physical centre of the lens.

Toric or sphero-cylindrical lenses have surfaces with two different radii of curvature in two orthogonal planes. They have a different focal power in different meridians. This forms an astigmatic lens. An example is eyeglass lenses that are used to correct astigmatism in someone's eye.

More complex are aspheric lenses. These are lenses where one or both surfaces have a shape that is neither spherical nor cylindrical. The more complicated shapes allow such lenses to form images with less aberration than standard simple lenses, but they are more difficult and expensive to produce.

Types of simple lenses

Biconvex lenses

Biconvex lenses are a simple lens comprising two convex spherical surfaces, generally with the same radius of curvature. Knight Optical supplies a wide range of stock and bespoke biconvex lenses, available coated or uncoated.

Bi-concave lenses

Bi-concave lenses have a negative focal length and are best used to diverge a converging beam. Bi-concave lenses can diverge a collimated beam to a virtual focus and are commonly used in Galilean-type beam expanders.

Lensmaker's equation

The focal length of a lens in air can be calculated from the lensmaker's equation

where

${\displaystyle f}$ is the focal length of the lens,

${\displaystyle n}$ is the refractive index of the lens material,

${\displaystyle R_{1}}$ is the radius of curvature (with sign, see below) of the lens surface closer to the light source,

${\displaystyle R_{2}}$ is the radius of curvature of the lens surface farther from the light source, and

${\displaystyle d}$ is the thickness of the lens (the distance along the lens axis between the two surface vertices).

The focal length f is positive for converging lenses, and negative for diverging lenses. The reciprocal of the focal length, 1/f, is the optical power of the lens. If the focal length is in metres, this gives the optical power in dioptres (inverse metres).

Lenses have the same focal length when light travels from the back to the front as when light goes from the front to the back. Other properties of the lens, such as the aberrations are not the same in both directions.