Lenses

by Chris Woodford. Last updated: December 15, 2021.

Microscopes let us peer inside invisible worlds our eyes could never see, telescopes take us far beyond the Earth to the stars and planets of the night sky, movie projectors throw enormous images onto screens, and lighthouses cast reassuring beams of light far across the ocean. Amazing curves of glass or plastic called lenses make all these things possible. Let's take a closer look at what they are and how they work!

Photo: Lenses can make things look bigger or smaller by making light rays appear to come from points nearer or further than they actually do. Photo by Joshua R. Maund courtesy of US Air Force and DVIDS.

What are lenses?

A lens is a transparent piece of glass or plastic with at least one curved surface. It gets its name from the Latin word for "lentil" (a type of pulse used in cooking), but don't let that confuse you. There's no real reason for this other than that the most common kind of lens (called a convex lens) looks very much like a lentil!

Photo: Lentils gave lenses their name. Convex lenses bulge out in the middle like lentils, while concave lenses "cave in" in the middle and bulge out at the edges.

How do lenses work?

A lens works by refraction: it bends light rays as they pass through it so they change direction. (You can read a full explanation of why this happens in our article on light.) That means the rays seem to come from a point that's closer or further away from where they actually originate—and that's what makes objects seen through a lens seem either bigger or smaller than they really are.

Types of lenses

There are two main types of lenses, known as convex (or converging) and concave (or diverging).

Convex lenses

In a convex lens (sometimes called a positive lens), the glass (or plastic) surfaces bulge outwards in the center giving the classic lentil-like shape. A convex lens is also called a converging lens because it makes parallel light rays passing through it bend inward and meet (converge) at a spot just beyond the lens known as the focal point.

Photo: A convex lens makes parallel light rays converge (come together) at the focal point or focus. The distance from the center of the lens to the focal point is the focal length of the lens. The focal point is on the opposite side of the lens to that from which the light rays originate.

Convex lenses are used in things like telescopes and binoculars to bring distant light rays to a focus in your eyes.

Concave lenses

A concave lens is exactly the opposite with the outer surfaces curving inward, so it makes parallel light rays curve outward or diverge. That's why concave lenses are sometimes called diverging lenses. (One easy way to remember the difference between concave and convex lenses is to think of concave lenses caving inwards.)

Photo: A concave lens makes parallel light rays diverge (spread out) so that they appear to come from a point behind the lens—the focal point. The distance from the center of the lens to the focal point is, again, the focal length of the lens. However, in this case, since the light rays don't really come from here, we call it a virtual focal point.

Concave lenses are used in things like TV projectors to make light rays spread out into the distance. In a flashlight, it's easier to do this job with a mirror, which usually weighs much less than a lens and is cheaper to manufacture as well.

Compound lenses

It's possible to make lenses that behave in more complex ways by combining convex and concave lenses. A lens that uses two or more simpler lenses in this way is called a compound lens.

How do you measure the power of a lens?

If you've ever looked through binoculars, a telescope, or a magnifying glass, you'll know that some lenses magnify (or reduce) the apparent size of an object much more than others. There's a simple measurement that tells you how powerful a lens is and it's known as the focal length. The focal length of a lens is the distance from the center of the lens to the point at which it focuses light rays. The shorter the focal length, the more powerful the lens. (It's easy to see why: an ordinary piece of glass would be like a lens of infinite focal length and wouldn't bring light rays to a focus at all. On the other hand, an infinitely powerful lens would bring lays rays to a focus in an infinitely short distance, with zero focal length. A real lens is somewhere between these two extremes.)

You'll find focal lengths written either in ordinary units of length (such as centimeters, millimeters, or inches) or in special optical units called diopters. The diopter measurement of a lens is the reciprocal of the focal length in meters (one divided by the focal length), so 1 diopter = 1 m, 2 diopters = 0.5 m, 3 diopters = 0.33 meters, and so on. Eyeglass prescriptions from opticians typically show the strength of the corrective lenses you need in diopters.

The focal length isn't the only important feature of a lens. Bigger lenses gather more light than smaller ones, so they make a brighter image. This is particularly important if you're choosing a lens for a camera, because the amount of light the lens gathers will determine what the image looks like. Camera lenses are usually rated with a measurement called the f-number, which is the focal length divided by the diameter. Generally speaking, lenses with a small f-number make brighter images. Lenses with a higher f-number have a bigger depth of focus: essentially, more of the object you're photographing and its surroundings are in focus at the same time. (If you want to know more, take a look at Louis Bloomfield's explanation of lens size.)

Adjustable lenses

Photo: The adjustable zoom lens on this Canon digital camera zooms three times (3×). Its focal length changes between 5.8–17.4mm, which is a ratio of 1:3.

An ordinary lens has a fixed focal length—so it does one job and one job only. But what if you want it to magnify a little bit more or focus on something slightly nearer or further away? Our own eyes (and brains) solve that problem with flexible lenses that can change shape under the control of the little ciliary muscles around them; stretching or squeezing the lenses changes their focal length.

What about binoculars, telescopes, and cameras, where the things you want to look at aren't always the same distance away?

For binoculars and telescopes, the solution is a focusing screw that moves the lenses in the tubes nearer to one another or further apart. Zoom lenses in cameras work in a similar way, with multiple lenses that can be moved together or apart by turning them with your fingers or, on automatic cameras, by pressing a motorized control that does the same thing. Zoom lenses that work this way are known as optical zooms. Digital zooms, in digital cameras, mimic the same process using computer software, effectively scaling up a smaller part of the original image (when they zoom in) or using a bigger part of that image (when they zoom out). Unlike optical zooms, digital zooms very quickly lose detail and blur images.

How are lenses made?

Photo: This magnifying glass uses a single convex lens made from plastic.

Until plastics became common in the 20th century, virtually all lenses were made by grinding solid pieces of glass into different shapes. Convex lenses were made by using a concave-shaped grinding tool (and vice-versa), and then the roughly shaped lens was polished to make its final shape. The ordinary glass we use in windows and crockery isn't good enough to use for lenses, because it contains air bubbles and other imperfections. These cause light rays to divert from their correct path, making a fuzzy image or one that makes different colors of light behave in different ways (problems that optical scientists refer to as aberrations). Instead, lenses are made using a more refined material known as optical glass. For eyeglasses, many people now prefer plastic lenses because they're much lighter and safer than optical glass. Plastic lenses can be molded to shape, instead of being ground, so they can be made in huge quantities far more cheaply than glass lenses. Although ordinary plastic scratches easily, it can be coated with a thin layer of a protective material such as diamond-like carbon (DLC) to reduce the risk of damage. Some optical lenses are also coated with thin plastic to reduce annoying reflections; you can read how these anti-reflective coatings work in our article on thin-film interference.

What are lenses used for?

Lenses are everywhere in the world around us—in everything from car headlamps and flashlights to the LED lights used in electronic instrument panels.

Photo: Lenses in the headlamps of this car focus beams of light down onto the road so you can see where you're going. Some car headlights use Fresnel lenses to make powerful beams, just like lighthouses!

Our eyes contain probably the most amazing lenses of all. Think what happens when you look at the world around you. One minute you're staring at the ground in front of your feet. Seconds later, you hear an airplane screaming past, turn your head, and watch it fly by. Do this trick with a pair of binoculars and you'll find it takes you quite a while to adjust the focus from near-sight (looking at the ground) to far (watching the plane). Try it with the naked eye and you won't even notice what you're doing. That's because your eyes have flexible lenses, controlled by tiny muscles, that can bulge in and out, changing shape instantly to focus on anything from the prints on your finger to the surface of the Moon. How amazing is that?

Photos: Lighthouses don't use huge and heavy lenses: instead, they rely on Fresnel lenses (ones with a stepped surface pattern of concentric rings) and prisms, like the one in this exhibit at Think Tank, the science museum in Birmingham, England. Read how they work in our article on Fresnel lenses.

We all have lenses in our eyes, but many of us balance extra ones on the end of our noses to correct long and short sight: more glass and plastic lenses are used for eyeglasses and contact lenses than for any other purpose. There are all kinds of eyeglass lenses, including light-sensitive photochromic ones that darken in sunlight and double-up as sunglasses.

You'll also find lenses in binoculars (which use two or three lenses in each of the cylinders serving your eyes) and telescopes, though not all microscopes use them. Ordinary (optical) microscopes use a series of glass lenses to magnify tiny objects, while super-powerful electron microscopes use electromagnets to bend electron beams that help us see in even more detail. Movie projectors and projection televisions use lenses to convert small movie pictures into giant images that lots of people can view at once. Cameras work the opposite way, catching light rays from a distance and bringing them to focus on chemically treated plastic film or light-sensitive electronic chips called CCDs. You can even find lenses built into magazine and book covers to make images change as you shift your head from side to side; this cunning trick is called lenticular printing—but it really just means "printing with built-in lenses."

What are lenses made from?

Photo: Plastic lenses: You might not have noticed, but the tiny LEDs (light-emitting diodes) used in instrument panels have tiny plastic lenses built into them to magnify the light they produce. The lens is the curved plastic bit on the left (the top of the LED that shines toward you.)

In two words, glass or plastic—although there's a bit more to it than that.

Obviously we have to make lenses from transparent things that don't distort the light rays passing through them—and there aren't really that many materials we can use. Early lenses were sometimes made from crystals; one of the oldest known, the Nimrud lens in the British Museum in London, is a piece of quartz (sometimes called "rock crystal") estimated to be 3000 years old and believed to have been used as a magnifying or burning glass, though its optical quality was very poor. More recently, Roman Emperor Nero reputedly used lenses made from emeralds to watch gladiators fighting to the death. Modern optical instruments like spectacles and telescopes became possible when people figured out how to make and use reliably high quality glass; spectacles date from about the 13th century and telescopes from the 17th century (pioneered by German-Dutch Hans Lippershey).

During the 20th century, cheap, lightweight, reliably made plastics became widely available and most low-cost optical devices now use plastic lenses (sometimes known as "organic glass"—made from materials such as polycarbonate) in place of glass ones (sometimes known as "mineral glass" to differentiate it from plastic equivalents). Disposable contact lenses, for example, became possible with the arrival of cheap, mass-produced, high-quality plastics—and, if you wear eyeglasses or have a camera on your phone, the lenses will almost certainly be plastic ones.

Photo: Plastic lenses, like the one in this magnifying glass, are much lighter and easier to hold for long periods, but they scratch much more easily.

Plastics, though cheap, certainly have their drawbacks: their optical quality is generally not as good as glass, they scratch very easily, they change their optical properties more readily than glass as the temperature changes, they don't transmit all light wavelengths as well as glass, and they don't always bend light as successfully (glass typically has a higher refractive index, although it is possible to use special, high refractive index plastic as an alternative if you want thin, light, eyeglass lenses). But let's not forget that glass has drawbacks too: its heavy (for example, in strong eyeglass prescriptions), expensive, and it can shatter (so glass eyeglasses were never great for playing sports). Ultimately, glass and plastics both have their pros and cons. As with anything else in the world of technology, we need to pick the best possible material for the job we need to do given the everyday, physical conditions it will have to perform under; that's what materials science is all about.

Find out more

On this website

We've got lots of other articles about optics, including:

• Binoculars
• Fiber optics
• Fresnel lenses
• Lasers
• Light
• Mirrors

For older readers

• Optics by Eugene Hecht. Addison-Wesley, 2016. A definitive undergraduate textbook on light.
• Photographic Lenses: Photographer's Guide to Characteristics, Quality, Use, and Design by Ernst Wildi. Amherst Media, 2001. Although aimed at photographers, this book gives a good overview of different types of lenses, how they differ, and what you can use them for.
• Leica Lens Practice: Choosing and Using Leica Lenses by Dennis Laney. Kogan Page, 2006. Another photographic book that will be of more general interest. Includes illustrated explanations of how different sized lenses produce different photographic effects.

For younger readers

• Everything You Need to Know About Lenses and Light by Baby Professor. Speedy Publishing, 2017. Ages 7–10.
• Science Pathways: Light by Chris Woodford. Rosen, 2013. This is one of my own books, and it describes how scientists have understood light and put it to use throughout history. Suitable for ages 9–12. (Previously published by Blackbirch, 2004.)
• Light by David Burnie. Dorling Kindersley, 1998. An introduction to the science, technology, and history of light from the popular DK Eyewitness series. For ages 9–12.

Articles

History

• How are spectacle lenses manufactured? by Zeiss, 28 March 2018. A fascinating article that walks us through the very precise process of creating eyeglass lenses.
• Johannes Hudde and His Flameworked Microscope Lenses by Marvin Bolt, Tiemen Cocquyt and Michael Korey, Journal of Glass Studies, Vol. 60 (2018), pp. 207–222. Although modern lenses are generally thin (loosely speaking, "flat"), back in the 17th-century, globe-shaped ball lenses were much more common.
• The problems with lenses, and the 19th-century solution: This article from Cambridge University's Whipple Museum explains why lenses distort images and how inventors got around the problem to make the first microscopes.
• The Invention of Spectacles: How and where Glasses may have begun.: The College of Optometrists charts eyeglasses back through history to the 13th century. [Archived via the Wayback Machine]
• Lenses in Antiquity by George Sines and Yannis A. Sakellarakis, American Journal of Archaeology, Vol. 91, No. 2, April 1987, pp. 191–196. The ancient history of lenses.

Popular science and news stories

• Who Made That Contact Lens? by Daniel Engber. The New York Times. April 13, 2014. The idea of using artificial (contact) lenses instead of eyeglasses dates back to at least the 19th century.
• Tiny Lenses See the Big Picture by Fenella Saunders, American Scientist, Vol. 101, No. 4, Jul-Aug 2013, pp.270–271. How the compound eyes of insects are inspiring powerful new lenses for digital cameras.
• Clearer Vision After Cataracts by Peter Jaret. The New York Times, May 15, 2009. The lenses in our eyes can degrade as we get older, turning cloudy as cataracts form. Fortunately, corrective lenses can solve the problem. [Archived via the Wayback Machine.]

Other useful websites

• Optics for Kids: Lots of good educational material from the Optical Society of America.
• The MusEYEum: A museum in London, England run by the College of Optometrists. The website includes quite a few online exhibits that are worth a browse.