Reading and translating the text Lenses

No doubt the most widely used optical device is the lens, and that notwithstanding the fact that we see the world through a pair of them. Lenses date back to the burning glasses of antiquity, and indeed who can say when people first peered through the liquid lens formed by a droplet of water.

Lenses are made in wide range of forms; for example, there are acoustic and microwave lenses; some of the latter are made of glass or wax in easily recognizable shapes, whereas others are far more subtle in appearance. In the traditional sense, a lens is an optical system consisting of two or more refracting interfaces, at least one of which is curved. Generally the nonplanar surfaces are centered on a common axis. These surfaces are most frequently spherical segments and are coated with thin dielectric filmes to control their transmission properties. A lens that consists of one element is a simple lens. The presence of more than one element makes it a compound lens. A lens is also classified as to whether it is thin or thick, that is, whether its thickness is effectively negligible or not. We will limit ourselves, for the most part, to centered systems (for which all surfaces are rotationally symmetric about a соmmon axis) of spherical surfaces. Under these restrictions, the simple lens can take the diverse forms. Lenses that are variously known as convex, converging, or positive are thicker at the center and so tend to decrease the radius of curvature of the wavefronts. In other words, the wave converges more as it traverses the lens, assuming, of course, that the index of the lens is greater than that of the media in which it .is immersed. Concave, diverging, or negative lenses, on the other hand, are thinner at the center and tend to advance that portion of wavefront, causing it diverge more than it did upon entry.

In the broadest sense, a lens is a refracting device that is used to reshape wavefronts in a controlled manner. Although this is usually done by passing the wave through at least one specially shaped interface separating two different homogeneous media it is not the only approach available. For example, it is also possible to reconfigure a wavefront by passing it through an inhomogeneous medium. A gradient-index, or GRIN, lens is one where the desired effect is accomplished by using medium in which the index of refraction varies in a prescribed fashion. Different portions of the wave propagate at different speeds, and the front changes shape as it progresses. In the commercial GRIN material the index varies radially, decreasing parabolically out from the central axis.

Today GRIN lenses are still fabricated in quantity only in the form of small-diameter, parallel, flat-faced rods. Usually grouped together in large arrays, they have been used extensively in such equipment as facsimile machines and compact copiers. There are other unconventional lenses, including the holographic lens and even the gravitational lens (where, for example, the gravity of galaxy bends light passing in its vicinity, thereby forming multiple images of a distant celestial object, such as quasars).

No lens is a thin lens, in the strict of having thickness that approaches zero. Yet many simple lenses, for all practical purposes, function in a fashion eqivalent to that of a thin lens. Almost all spectacle lenses, which, by the way, have been used at least since the thirteenth century, are in this category. When the radii of curvature are large and the lens diameter is small, the thickness will usually be small as well. A lens of this sort would generally have a large focal length, compared with which the thickness would be quite small; many early telescope objectives fit that description perfectly.