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A lens (or '''lense''') is an lens can be made from Paraffin Wax . HISTORY See Also: History of optics The oldest lens artefact is dated to c., 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 . The ( 965 – 1038 ) wrote the first major Optical treatise, the '' Book Of Optics '', which described how the Lens in the human Eye formed an image on the Retina . 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 concentrate sunlight enough to ignite fires. Widespread use of lenses did not occur until the use of Reading Stone s in the 11th century and the invention of Spectacles , probably in Italy in the 1280s . 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. CONSTRUCTION OF SIMPLE LENSES as seen through a lens.]] Most lenses are spherical lenses: their two surfaces are parts, with the same axis as each other, of the surfaces of spheres. Each surface can be (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 simple lenses Lenses are classified by the curvature of the two optical surfaces. A lens is biconvex (or '''double convex''', or just '''convex''') if both surfaces are convex, 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''' or ''meniscus''. 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:Greivenkamp, p.14; Hecht §6.1 : where : is the focal length of the lens, : is the Refractive Index of the lens material, : is the radius of curvature of the lens surface closest to the light source, : is the radius of curvature of the lens surface farthest from the light source, and : is the thickness of the lens (the distance along the lens axis between the two Surface Vertices ). Sign convention of lens radii ''R''1 and ''R''2 See Also: Radius of curvature (optics) The signs of the lens' radii of curvature indicate whether the corresponding surfaces are convex or concave. The , the corresponding surface is flat. Thin lens equation If ''d'' is small compared to ''R''1 and ''R''2, then the '' Thin Lens '' approximation can be made. For a lens in air, ''f'' is then given by : Hecht, § 5.2.3 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 '' Dioptre s'', 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. IMAGING PROPERTIES As mentioned above, a positive or converging lens in air will focus a collimated beam travelling along the lens axis to a spot (known as the Focal Point ) at a distance ''f'' from the lens. Conversely, a Point Source of light placed at the focal point will be converted into a collimated beam by the lens. These two cases are examples of Image formation in lenses. In the former case, an object at an infinite distance (as represented by a collimated beam of waves) is focused to an image at the focal point of the lens. In the latter, an object at the focal length distance from the lens is imaged at infinity. The plane perpendicular to the lens axis situated at a distance ''f'' from the lens is called the ''focal plane''. If the distances from the object to the lens and from the lens to the image are ''S''1 and ''S''2 respectively, for a lens of negligible thickness, in air, the distances are related by the thin lens formula: : . What this means is that, if an object is placed at a distance ''S''1 along the axis in front of a positive lens of focal length ''f'', a screen placed at a distance ''S''2 behind the lens will have an image of the object projected onto it, as long as ''S''1 > ''f''. This is the principle behind Photography . The image in this case is known as a '' Real Image ''. Note that if ''S''1 < ''f'', ''S''2 becomes negative, the image is apparently positioned on the same side of the lens as the object. Although this kind of image, known as a '' Virtual Image '', cannot be projected on a screen, an observer looking through the lens will see the image in its apparent calculated position. A Magnifying Glass creates this kind of image. The '' Magnification '' of the lens is given by: : , |
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