::Anatomy of a Lens::

If a piece of glass or other transparent material takes on the appropriate shape, it is possible that parallel incident rays would either converge to a point or appear to be diverging from a point. A piece of glass that has such a shape is referred to as a lens.

A lens is merely a carefully ground or molded piece of transparent material that refracts light rays in such as way as to form an image. Lenses can be thought of as a series of tiny refracting prisms, each of which refracts light to produce their own image. When these prisms act together, they produce a bright image focused at a point.There are a variety of types of lenses. Lenses differ from one another in terms of their shape and the materials from which they are made. Our focus will be upon lenses that are symmetrical across their horizontal axis - known as the principal axis. In this unit, we will categorize lenses as converging lenses and diverging lenses. A converging lens is a lens that converges rays of light that are traveling parallel to its principal axis. Converging lenses can be identified by their shape; they are relatively thick across their middle and thin at their upper and lower edges. A diverging lens is a lens that diverges rays of light that are traveling parallel to its principal axis. Diverging lenses can also be identified by their shape; they are relatively thin across their middle and thick at their upper and lower edges.
A double convex lens is symmetrical across both its horizontal and vertical axis. Each of the lens' two faces can be thought of as originally being part of a sphere. The fact that a double convex lens is thicker across its middle is an indicator that it will converge rays of light that travel parallel to its principal axis. A double convex lens is a converging lens. A double concave lens is also symmetrical across both its horizontal and vertical axis. The two faces of a double concave lens can be thought of as originally being part of a sphere. The fact that a double concave lens is thinner across its middle is an indicator that it will diverge rays of light that travel parallel to its principal axis. A double concave lens is a diverging lens. These two types of lenses - a double convex and a double concave lens will be the only types of lenses that will be discussed in this unit of The Physics Classroom Tutorial. As we begin to discuss the refraction of light rays and the formation of images by these two types of lenses, we will need to use a variety of terms. Many of these terms should be familiar to you because they have already been discussed during Unit 13. If you are uncertain of the meaning of the terms, spend some time reviewing them so that their meaning is firmly internalized in your mind. They will be essential as we proceed through Lesson 5. These terms describe the various parts of a lens and include such words as

Principal axis	Vertical Plane
Focal Point	Focal Length

If a symmetrical lens were thought of as being a slice of a sphere, then there would be a line passing through the center of the sphere and attaching to the mirror in the exact center of the lens. This imaginary line is known as the principal axis. A lens also has an imaginary vertical axis that bisects the symmetrical lens into halves. As mentioned above, light rays incident towards either face of the lens and traveling parallel to the principal axis will either converge or diverge. If the light rays converge (as in a converging lens), then they will converge to a point. This point is known as the focal point of the converging lens. If the light rays diverge (as in a diverging lens), then the diverging rays can be traced backwards until they intersect at a point. This intersection point is known as the focal point of a diverging lens. The focal point is denoted by the letter F on the diagrams below. Note that each lens has two focal points - one on each side of the lens. Unlike mirrors, lenses can allow light to pass through either face, depending on where the incident rays are coming from. Subsequently, every lens has two possible focal points. The distance from the mirror to the focal point is known as the focal length (abbreviated by f). Technically, a lens does not have a center of curvature (at least not one that has any importance to our discussion). However a lens does have an imaginary point that we refer to as the 2F point. This is the point on the principal axis that is twice as far from the vertical axis as the focal point is.
As we discuss the characteristics of images produced by converging and diverging lenses, these vocabulary terms will become increasingly important.

Lens History

The word lens comes from the Latin name of the lentil, because a double-convex lens is lentil-shaped. The genus of the lentil plant is Lens, and the most commonly eaten species is Lens culinaris. The lentil plant also gives its name to a geometric figure.
The oldest lens artifact is the Nimrud lens, which is over three thousand years old, dating back to ancient Assyria.^[3] David Brewster proposed that it may have been used as a magnifying glass, or as a burning-glass to start fires by concentrating sunlight.^[3][4] Assyrian craftsmen made intricate engravings, and could have used such a lens in their work. Another early reference to magnification dates back to ancient Egyptian hieroglyphs in the 8th century BC, which depict "simple glass meniscal lenses".^[5]
The earliest written records of lenses date to Ancient Greece, with Aristophanes' play The Clouds (424 BC) mentioning a burning-glass (a biconvex lens used to focus the sun's rays to produce fire). The writings of Pliny the Elder (23–79) also show that burning-glasses were known to the Roman Empire,^[6] and mentions what is arguably the earliest use of a corrective lens: Nero was said to watch the gladiatorial games using an emerald^[7] (presumably concave to correct for myopia, though the reference is vague). Both Pliny and Seneca the Younger (3 BC–65) described the magnifying effect of a glass globe filled with water.
In the 10th century, Ibn Sahl used what is now known as Snell's law to calculate the shape of lenses.^[8]
Excavations at the Viking harbour town of Fröjel, Gotland, Sweden discovered in 1999 the rock crystal Visby lenses, produced by turning on pole-lathes at Fröjel in the 11th to 12th century, with an imaging quality comparable to that of 1950s aspheric lenses. The Viking lenses were capable of concentrating enough sunlight to ignite fires.^[9]
Widespread use of lenses did not occur until the use of reading stones in the 11th century and the invention of spectacles, probably in Italy in the 1280s. Scholars have noted that spectacles were invented not long after the translation of Ibn al-Haytham's Book of Optics into Latin, but it is not clear what role, if any, the optical theory of the time played in the discovery.^[5][10] Nicholas of Cusa is believed to have been the first to discover the benefits of concave lenses for the treatment of myopia in 1451.
The Abbe sine condition, due to Ernst Abbe (1860s), is a condition that must be fulfilled by a lens or other optical system in order for it to produce sharp images of off-axis as well as on-axis objects. It revolutionized the design of optical instruments such as microscopes, and helped to establish the Carl Zeiss company as a leading supplier of optical instruments.