Lens Theory

Fig. 1 is a common diagram used to define quantities for the analysis of a singlet lens. The quantities defined can also be extended to multi-
element systems by procedures outlined in optical design textbooks.

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The optical axis (O-O&#;) of the lens is a line passing through the centers of curvature of the two spherical lens surfaces (centers of curvature not shown). 
Ray A is incident from left to right and parallel to the optical axis. Ray A is refracted to point F2 on axis, the back, second, or secondary focal point. 
Ray B is incident from right to left and parallel to the optical axis. Ray B is refracted to point F1 on axis, the front, first, or primary focal point.
Suppose the lens is &#;well-corrected&#;. That means all rays A parallel to the axis are focused to a single point F2, regardless of their distance from the axis. It is clear then that the family of rays refracted to F2 intersect the family of progenitor rays A in a sphere centered at F2. This sphere, or, in general, surface of intersection of progenitor and refracted rays is called the back, second, or secondary principal surface. The intersection H2 of this surface with the optical axis is called the back, second, or secondary principal point.

Similarly, rays B incident from the right, and their refracted rays impinging on F1, intersect to form a front, first, or primary principal surface, which intersects the optical axis at H1, the front, first, or primary principal point.
In the paraxial approximation, all ray angles are small. This
approximation permits the modelling of the principal surfaces as
principal planes. The distances from the front and back principal points to their respective focal points are equal and given by f , the focal length or effective focal length. The front and back focal distances FFD and BFD, respectively, are measured from the surface intersections V1 and V2 to the respective focii. V1 and V2 are called the front and back vertices.
 

OPTICAL LENSES AND CONVEX/CONCAVE MIRROR THEORY

Optical lenses are polished glass or plastic substrates that are shaped with one or more curved surfaces that transmit light. Optical lenses may be used either uncoated or with an antireflective coating depending on their intended application.

All optical lenses have a focal length which is the distance from the lens to the focal point along the optical axis of the lens. Three factors determine the focal length of a lens; the radius of curvature of the lens, the refractive index of the substrate from which the lens is made, and the medium in which the lens resides. Lenses that are highly curved and made from material with a high refractive index, and placed in a medium with a large difference in the refractive index will have a shorter focal length and will therefore be more powerful. The focal length of a lens can be calculated using the lens maker&#;s formula.

Convex Lenses

Convex lenses bulge outward from the center and converge light rays parallel to the optical axis to a focal point beyond the lens. Therefore, they may also be referred to as positive or converging lenses. The focal point is the point where the collimated light rays converge and come into focus.

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Convex lenses can be manufactured in different configurations such as; biconvex, plano-convex, or as a positive meniscus.

Concave Lenses

Concave lenses curve inward from the center and diverge light rays parallel to the optical axis from a focal point behind the lens. Therefore, they may also be referred to as negative or diverging lenses. The focal point is the point where the collimated light rays appear to diverge from after passing through the lens.

Concave lenses can be manufactured in different configurations such as; biconcave, plano-concave, or as a negative meniscus.

Convex/Concave Mirrors

Optical lenses can be made into convex and concave mirrors by the addition of a reflective coating. However, as the mirror is reflecting light, as opposed to transmitting light, the focal point is reversed. As with lenses, the more curved the mirror is, the shorter its focal length will be, and hence the more powerful the mirror will be.

Convex Mirrors

Convex mirrors (Diverging Mirrors) have a surface that is curved outward so that collimated light diverges away from the reflective surface. The focal point is located behind the mirror and is referred to as a negative focal point. It is the point from which the light appears to have originated after reflection from the mirror.

Concave Mirrors

Concave mirrors (Focusing Mirrors) have a surface that is curved inward and therefore collects collimated light. The focal point is located in front of the mirror and is referred to as a positive focal point. It is the point at which the parallel beams of light focus after reflection from the mirror.

Advanced Optics custom manufactures glass convex and concave lenses and mirrors from 6mm to 530mm that can be purchased either uncoated or with a variety of coatings for use in the UV-VIS-NIR spectrum. To learn more about our capabilities and how to correctly specify the proper optic for your system, please visit our page Optical Lenses and Convex/Concave Mirrors for further information.

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