Lenses

A lens is a curved piece of glass or plastic that bends light by refraction. Different shapes of lens do different things: some focus light to a point, others spread it out. By choosing the right shape and material, lens makers can build devices that magnify tiny things (microscopes), reach distant things (telescopes), capture sharp images (cameras), help our eyes see clearly (glasses) and project light in beams (torches and projectors). The eye in your head is a lens too: one of the most sophisticated natural optical devices in the world.

• What it doesBends light by refractionTo focus, magnify or spread
• Convex lensThicker in middleBrings light to a point
• Concave lensThinner in middleSpreads light apart
• Used inEyes, glasses, camerasPlus microscopes and telescopes
• Focal lengthDistance to focal pointShorter = more powerful
• First eyeglassesItaly, around 1290Convex lenses for reading

Two main shapes

Convex lens: thicker in the middle than at the edges. It bends parallel light inwards to meet at a single point called the focal point. Convex lenses are used to:

• Magnify (magnifying glasses, reading glasses for long-sightedness).
• Focus light onto a screen, sensor or retina.
• Form sharp images in cameras, projectors and telescopes.

Concave lens: thinner in the middle than at the edges. It spreads parallel light outward, as if the light came from a point behind the lens. Concave lenses are used to:

• Help nearsighted people see distant objects (the glasses lens makes light less converged before it reaches the eye).
• Reduce magnification in some telescopes and microscopes.
• Spread laser beams over a wider area.

Focal length

The focal length of a lens is the distance from the lens to its focal point (for a convex lens) or to the virtual focal point (for a concave lens). A short focal length means the lens bends light more strongly: a "powerful" lens. Long focal length means weak bending.

Glasses prescriptions are measured in dioptres, which equal 1 divided by the focal length in metres. A 1-dioptre lens has a 1-metre focal length; a 5-dioptre lens has a 20-cm focal length and bends light 5 times more strongly. Negative dioptres mean concave (spreading) lenses for short-sightedness.

Fact The first eyeglasses were probably invented in northern Italy around 1290, using two small convex lenses set in a frame. They were used by monks and scholars to read in old age, when natural lens flexibility weakens. Until the invention of the printing press 150 years later, books were rare and reading was a job for specialists, so glasses were only useful to a tiny fraction of people. With printed books, glasses became widely useful and have stayed that way ever since.

Lenses everywhere

• Eyes: every eye contains a flexible lens that adjusts its shape to focus on objects at different distances.
• Glasses and contact lenses: correct vision problems with carefully designed lenses.
• Cameras: a lens (or a combination of several) focuses an image onto film or a digital sensor. Phone cameras now contain multiple tiny lenses in a stack.
• Microscopes: typically two convex lenses (or more) magnify tiny objects.
• Telescopes: collect light from distant objects. Refracting telescopes use a big convex lens at the front; reflecting ones use mirrors instead.
• Magnifying glasses: a single convex lens.
• Projectors: a strong light shines through a slide or LCD screen, and a lens projects the image onto a screen.
• Binoculars: pairs of lenses (one for each eye) with internal prisms.
• Lasers: lenses focus and direct laser beams.
• Lighthouses: huge Fresnel lenses focus a small light source into a bright beam visible for many kilometres.

How an eye lens works

The lens inside your eye is a small soft disc made mostly of clear protein. Tiny muscles attached to its edge can pull or relax the lens, changing its shape:

• To look at something close, the muscles relax and the lens becomes more curved (more refractive power).
• To look at something far, the muscles tense up and the lens flattens (less refractive power).

This automatic process is called accommodation. It happens without you thinking. As people age, the lens gradually stiffens, losing its ability to bend for close objects. Most people start needing reading glasses in their forties.

Common vision problems and their lenses

• Short-sightedness (myopia): distant things look blurry. The eye is too long, so light focuses just before the retina. Concave (negative) lenses spread the light before it enters the eye, helping it focus on the retina.
• Long-sightedness (hyperopia): close things look blurry. The eye is too short, so light focuses just behind the retina. Convex (positive) lenses help the eye focus closer.
• Astigmatism: the cornea is not perfectly round, so light focuses unevenly. Cylindrical lenses (curved in one direction only) correct it.
• Presbyopia: the age-related stiffening of the eye lens. Treated with reading glasses (convex) or bifocals/varifocals.

Did you know? The biggest single lens ever made is in the Yerkes Observatory in Wisconsin, USA. It is 1 metre across, made in 1897, and has not been replaced because glass lenses sag under their own weight when they get too big. For larger telescopes, astronomers switched to using mirrors. The Yerkes lens is still in operation as a historic instrument.

Making a lens

Lens-making is precise work. The basic steps:

• Cut a disc of high-quality optical glass.
• Grind the surfaces to roughly the right curve using harder abrasives.
• Polish to high optical smoothness (the surfaces have to be perfect to within a fraction of the wavelength of light).
• Apply an antireflective coating (a few atoms thick) to reduce glare.
• Quality-check using interferometers and laser test rigs.

Plastic lenses (used for many ordinary spectacles, contact lenses and phone cameras) are made by moulding from precisely-shaped tools. Cheaper and faster, but not as durable or precise as glass.

Try this Use a strong convex magnifying glass to focus sunlight to a tiny point on a piece of paper (with adult supervision and outdoors). The paper can heat enough to scorch or even catch fire (so do not point the focused light at anything else; never at your eyes; never at human skin or animals). You have just used refraction to focus the suns parallel rays to the lens focal point, concentrating all that sunlight into a tiny spot.

Deeper dive: how camera lenses got so good

The lens in a modern smartphone camera is one of the most sophisticated optical devices ever made for the consumer market. Inside a tiny module barely a centimetre across, multiple lens elements work together to capture sharp, full-colour images of nearly any scene.

Just one lens can never produce a perfect image. Several errors limit it:

• Spherical aberration: light at the edge of a simple lens focuses at a slightly different distance from light at the centre, blurring the image.
• Chromatic aberration: different colours of light focus at slightly different distances, giving coloured fringes around objects.
• Field curvature: a flat object can focus into a curved image, blurring at the edges.
• Distortion: straight lines bend into curves, like in fish-eye lenses (intentional there).

Professional photo lenses solve these problems using multiple elements: anywhere from 5 to 20 individual lenses of different shapes, materials and coatings, working together to cancel out each others errors. A single high-end camera lens can contain 15+ elements, each precisely shaped to a fraction of a wavelength.

Modern smartphone lenses are even more crammed. The latest iPhone main camera has a 7-element lens stack in a module smaller than a fingernail. The pieces are made of injection-moulded plastic with sub-micron precision. To improve image quality further, phone cameras now use computational photography: the lens hardware is helped by software that combines multiple exposures, sharpens detail, and corrects remaining lens errors in real time.

The result is that the camera in your pocket is now sharper than a 1960s news camera that cost a thousand times more in todays money. All built around the same idea Italian craftsmen tried in 1290: a curved piece of glass that bends light just so.

For more, see refraction and mirrors.