Lens

Lenses are made from materials such as glass or plastic and are ground, polished, or molded to the required shape.

[a] Some scholars argue that the archeological evidence indicates that there was widespread use of lenses in antiquity, spanning several millennia.

[5][verification needed] The oldest certain reference to the use of lenses is from Aristophanes' play The Clouds (424 BCE) mentioning a burning-glass.

[8] Both Pliny and Seneca the Younger (3 BC–65 AD) described the magnifying effect of a glass globe filled with water.

[9] Spectacles were invented as an improvement of the "reading stones" of the high medieval period in Northern Italy in the second half of the 13th century.

[10] This was the start of the optical industry of grinding and polishing lenses for spectacles, first in Venice and Florence in the late 13th century,[11] and later in the spectacle-making centres in both the Netherlands and Germany.

[13][14] The practical development and experimentation with lenses led to the invention of the compound optical microscope around 1595, and the refracting telescope in 1608, both of which appeared in the spectacle-making centres in the Netherlands.

[15][16] With the invention of the telescope and microscope there was a great deal of experimentation with lens shapes in the 17th and early 18th centuries by those trying to correct chromatic errors seen in lenses.

Opticians tried to construct lenses of varying forms of curvature, wrongly assuming errors arose from defects in the spherical figure of their surfaces.

[17] Optical theory on refraction and experimentation was showing no single-element lens could bring all colours to a focus.

Developments in transatlantic commerce were the impetus for the construction of modern lighthouses in the 18th century, which utilize a combination of elevated sightlines, lighting sources, and lenses to provide navigational aid overseas.

Fresnel lens were developed that considered these constraints by featuring less material through their concentric annular sectioning.

A ball-shaped lens has the advantage of being omnidirectional, but for most optical glass types, its focal point lies close to the ball's surface.

Due to paraxial approximation where the line of h is close to the vertex of the spherical surface meeting the optical axis on the left,

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 some cases, S2 is negative, indicating that the image is formed on the opposite side of the lens from where those rays are being considered.

Rather, the plate scale of the camera is about 1°/mm, from which one can conclude that the 0.5 mm image on the film corresponds to an angular size of the moon seen from earth of about 0.5°.

In fact, the diameter of the projected spot is not actually zero, since diffraction places a lower limit on the size of the point spread function.

Spherical aberration can be minimised with normal lens shapes by carefully choosing the surface curvatures for a particular application.

As with spherical aberration, coma can be minimised (and in some cases eliminated) by choosing the curvature of the two lens surfaces to match the application.

Chromatic aberration is caused by the dispersion of the lens material—the variation of its refractive index, n, with the wavelength of light.

Different lens materials may also be used to minimise chromatic aberration, such as specialised coatings or lenses made from the crystal fluorite.

This naturally occurring substance has the highest known Abbe number, indicating that the material has low dispersion.

A diffraction-limited lens is one in which aberrations have been reduced to the point where the image quality is primarily limited by diffraction under the design conditions.

[23] If the separation distance between two lenses is equal to the sum of their focal lengths (d = f1 + f2), then the FFD and BFD are infinite.

Note the sign convention: a telescope with two convex lenses (f1 > 0, f2 > 0) produces a negative magnification, indicating an inverted image.

These were formerly complex to make and often extremely expensive, but advances in technology have greatly reduced the manufacturing cost for such lenses.

It images a point source into a line along the optic axis, or transforms a laser beam into a ring.

Superlenses are made from negative index metamaterials and claim to produce images at spatial resolutions exceeding the diffraction limit.

They are usually shaped to fit in a roughly oval, not circular, frame; the optical centres are placed over the eyeballs; their curvature may not be axially symmetric to correct for astigmatism.