Lens
The lens takes its name from a seed. The Latin word lens means lentil, and a double-convex lens has the rounded, swollen shape of a lentil sitting in your palm. That humble naming hides a long and contested history. Some scholars insist that ground and polished lenses were in widespread use across antiquity, spanning several millennia. Others counter that most ancient so-called lenses were decorative trinkets, not working optics, with the exception of a few burning glasses. How did a piece of shaped glass move from a curiosity that could set wood alight to the precision element inside telescopes, microscopes, cameras, and the eyeglasses on countless faces? And why, for centuries, did the people who built the best lenses not understand how their own lenses worked?
Aristophanes put a lens on stage. His play The Clouds, from 424 BCE, contains the oldest certain reference to using a lens as a burning glass, which makes the device at least 2400 years old. Long before that play, the Nimrud lens, a rock crystal artifact dated to the 7th century BCE, was shaped in a way that may or may not have served as a magnifying glass or burning glass.
Pliny the Elder, writing in the 1st century, confirmed that burning glasses were known in the Roman period. He also recorded that Nero was said to watch gladiatorial games through an emerald, a passage some read as an early corrective lens for nearsightedness, though the reference is confusing and the interpretation has been disputed. Seneca the Younger described how letters, however minute and obscure, are perceived larger and clearer through a glass sphere filled with water, and how fruit floating in glass seems more shapely than it really is. These were observations of magnification without a theory to explain it. That gap between seeing the effect and understanding the cause would shape the next thousand years of lens making.
Between the 11th and 13th centuries, people read through stones. These reading stones were primitive plano-convex lenses, made at first by cutting a glass sphere in half and laying the curved glass over the page. The rock crystal Visby lenses, dated to the 11th or 12th century, belong to this murky era, and even they may or may not have been intended as burning glasses.
Spectacles grew directly out of those reading stones. They were invented in Northern Italy in the second half of the 13th century, and with them came an industry of grinding and polishing lenses, first in Venice and Florence in the late 13th century. The craft later spread to spectacle-making centres in the Netherlands and Germany. The makers improved their lenses by watching what the lenses did, gathering empirical knowledge rather than applying the rudimentary optical theory of the day. That hands-on tinkering paid off twice over. Around 1595 the compound optical microscope appeared, and in 1608 the refracting telescope followed, both emerging from the spectacle-making centres of the Netherlands.
In the 17th and early 18th centuries, opticians went to war with colour. The new telescopes and microscopes revealed coloured fringes around their images, and makers tried to grind lenses in varying curvatures to chase the problem away. They were wrong about its source. They assumed the errors came from defects in the spherical figure of their surfaces, when in fact no single-element lens could bring all colours to a single focus.
The fix was to combine materials, not perfect a curve. Chester Moore Hall invented the compound achromatic lens in England in 1733, joining two materials of differing dispersion so their colour errors partly cancelled. The same invention was later claimed by a fellow Englishman, John Dollond, in a 1758 patent. An achromat does not produce perfect correction, but it reduces chromatic aberration over a range of wavelengths, and its arrival was an important step in developing the optical microscope. A still better solution, the apochromat, corrects chromatic aberration even further and improves spherical aberration too, at a much higher price.
Transatlantic commerce demanded brighter lighthouses, and a conventional lens could not meet the demand without becoming enormous. To throw a beam the maximum distance needed for navigation at sea, a plain convex lens would have to be so large that it strained the cost, design, and construction of the lighthouse itself.
The Fresnel lens solved this by removing glass rather than adding it. Its surface is divided into concentric annular sections, so it uses far less material while keeping its focusing power. This same ring principle makes the lens much thinner and lighter than a conventional one. The first full implementation of a Fresnel lens in a lighthouse came in 1823. The design proved so practical that durable Fresnel lenses can now be molded cheaply from plastic, and the broken-up ring surface reappears in everyday optics far from any shoreline.
Most lenses are built from pieces of spheres. Each of a simple lens's two surfaces is part of the surface of a sphere, and each can bulge outward as convex, dip inward as concave, or sit flat as planar. The line joining the centres of those spheres is the axis of the lens, and it usually runs through the physical centre because of how lenses are made.
The combination of the two surfaces gives every simple lens its character and its name. A lens with two convex faces is biconvex, and if both faces share the same radius of curvature it is equiconvex. Two concave faces make a biconcave lens. One flat face produces a plano-convex or plano-concave lens, while one convex and one concave face make a meniscus, the shape favoured in corrective lenses because it minimizes some aberrations. Toric or sphero-cylindrical lenses break the symmetry further, carrying two different radii of curvature in two orthogonal planes, which gives them different focal power in different meridians. That astigmatic shape is exactly what eyeglass makers use to correct astigmatism in a wearer's eye.
Send a collimated beam through a biconvex lens sitting in a lower-index medium, and it bends inward to a single spot. That spot is the focus, and a lens that gathers light this way is called a positive or converging lens. For a thin lens in air, the distance from the lens to that spot is the focal length, written as f. A point source placed at the focal point reverses the trick, leaving the lens as a collimated beam.
A concave lens does the opposite. A biconcave or plano-concave lens in a lower-index medium spreads a collimated beam, earning the name negative or diverging lens, with a focal length counted as negative. Strangely, the rules invert when the lens sits in a medium of higher refractive index than its own material, so a biconvex lens there diverges light and a biconcave one converges it. The behaviour also branches into real and virtual images. A real image, like the one a camera throws onto its sensor or the eye casts onto the retina, can land on a screen, while a virtual image, like the magnified picture you see through a magnifying glass, only appears to float where no light actually gathers. For a given lens of focal length f, the minimum distance between an object and its real image is 4f.
No lens makes a perfect image. Every lens introduces some distortion or aberration, so the image is always an imperfect replica of the object, and careful design only minimizes the flaws. Spherical aberration arises because a sphere is not the ideal lens shape, merely the easiest to grind and polish, so rays far from the axis focus in a slightly different place than rays near it and blur the result.
Coma borrows its name from the comet. When an off-axis object is imaged, parallel rays passing through the lens at a fixed distance from its centre focus into a ring called a comatic circle, and all those rings stack into a V-shaped, comet-like flare. Lenses that minimize both spherical aberration and coma are called bestform lenses. Chromatic aberration, the coloured fringing, springs from dispersion, the way refractive index varies with wavelength. It can be tamed with the crystal fluorite, a naturally occurring substance with the highest known Abbe number and very low dispersion. Yet even a lens scrubbed of every aberration meets a final wall. Diffraction through the lens's finite aperture sets a floor on sharpness, and a lens that reaches it is called diffraction-limited. The lens that began as a lentil-shaped novelty now lives at the edge of what physics will allow, where the only blur left to fight is the spreading of light itself.
Common questions
What is a lens and how does a lens work?
A lens is a transmissive optical device that focuses or disperses a light beam by means of refraction. A simple lens is a single piece of transparent material, while a compound lens combines several simple lenses arranged along a common axis. Lenses are made from materials such as glass or plastic and are ground, polished, or molded to shape.
Where does the word lens come from?
The word lens comes from lens, the Latin name of the lentil, because a double-convex lens is lentil-shaped. The lentil also gives its name to a geometric figure.
How old is the use of lenses as burning glasses?
Lenses have been used as burning glasses for at least 2400 years. The oldest certain reference is in Aristophanes's play The Clouds, from 424 BCE.
When were spectacles invented?
Spectacles were invented in Northern Italy in the second half of the 13th century as an improvement on the reading stones of the high medieval period. This began the optical industry of grinding and polishing lenses, first in Venice and Florence in the late 13th century.
Who invented the achromatic lens?
Chester Moore Hall invented the compound achromatic lens in England in 1733. The same invention was also claimed by fellow Englishman John Dollond in a 1758 patent.
What is a Fresnel lens and when was it first used in a lighthouse?
A Fresnel lens has its optical surface broken into narrow concentric rings, allowing it to be much thinner and lighter while using less material. It was first fully implemented in a lighthouse in 1823.
What is the difference between a converging lens and a diverging lens?
A converging or positive lens, such as a biconvex lens in a lower-index medium, focuses a collimated beam to a spot behind the lens. A diverging or negative lens, such as a biconcave lens, spreads a collimated beam and has a negative focal length.
What are the main types of lens aberration?
The main aberrations are spherical aberration, coma, and chromatic aberration. Other kinds include field curvature, barrel and pincushion distortion, and astigmatism, and even a flawless lens is limited by diffraction through its finite aperture.