^_^LENS^_^

lens is a device that causes light to either converge and concentrate or to diverge. It is usually formed from a piece of shaped glass or plastic. Analogous devices used with other types of electromagnetic radiation are also called lenses: for instance, a microwave lens can be made from paraffin wax.

LENS CONSTRUCTION

Most lenses are spherical lenses: lenses whose surfaces have spherical curvature, that is, the front and back surfaces of the lens can each be imagined to be part of the surface of a sphere. 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; in almost all cases the lens axis passes through the physical centre of the lens.

Types of lenses
Lenses are classified by the curvature of the two optical surfaces. A lens is biconvex (also called double convex, or just convex) if both surfaces are convex, likewise, a lens with two concave surfaces is biconcave (or just concave). If one of the surfaces is flat, the lens is plano-convex or plano-concave depending on the curvature of the other surface. A lens with one convex and one concave side is convex-concave, and in this case if both curvatures are equal it is a meniscus lens. (Sometimes, meniscus lens can refer to any lens of the convex-concave type).

If the lens is biconvex or plano-convex, a collimated or parallel beam of light travelling parallel to the lens axis and passing through the lens will be converged (or focused) to a spot on the axis, at a certain distance behind the lens (known as the focal length). In this case, the lens is called a positive or converging lens.


If the lens is biconcave or plano-concave, a collimated beam of light passing through the lens is diverged (spread); 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 distance 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 (a meniscus lens), 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.

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

where:
f is the focal length of the lens,
n is the refractive index of the lens material,
R1 is the radius of curvature of the lens surface closest to the light source,
R2 is the radius of curvature of the lens surface farthest from the light source, and
d is the thickness of the lens (the distance along the lens axis between the two surface vertices).

Sign convention of lens radii R1 and R2

The signs of the lens' radii of curvature indicate whether the corresponding surfaces are convex or concave. The sign convention used to represent this varies, but in this article if R1 is positive the first surface is convex, and if R1 is negative the surface is concave. The signs are reversed for the back surface of the lens: if R2 is positive the surface is concave, and if R2 is negative the surface is convex. If either radius is infinite, the corresponding surface is flat.

Thin lens equation
If d is small compared to R1 and R2, then the thin lens approximation can be made. For a lens in air, f is then given by

The focal length f is positive for converging lenses, negative for diverging lenses, and infinite for meniscus lenses. The value 1/f is known as the optical power of the lens, and so meniscus lenses are said to have zero power. Lens power is measured in dioptres, which are units equal to inverse meters (m−1).
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, although other properties of the lens, such as the aberrations are not necessarily the same in both directions.