Lens

A lens is a transmissive optical device that focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (elements), usually arranged along a common axis. Lenses are made from materials such as glass or plastic and are ground, polished, or molded to the required shape.

A burning apparatus consisting of two biconvex lens

Lenses are used in various imaging devices such as telescopes, binoculars, and cameras. They are also used as visual aids in glasses to correct defects of vision such as myopia and hypermetropia. A lens can focus light to form an image, unlike a prism, which refracts light without focusing.

History

See also: History of optics and Camera lens

Light being refracted by a spherical glass container full of water. Roger Bacon, 13th century

The word lens comes from the Latin name for the lentil plant, because early lenses were shaped like this seed. Ancient people may have used simple lenses for making fire or as decorations, but it is unclear how often they were used for seeing better.

One of the oldest known lenses, the Nimrud lens, dates back to the 7th century BCE. Over time, people learned to make better lenses for reading and for seeing far away. By the 1200s, spectacle glasses were being made in places like Italy, Venice, and Florence. Later, these skills led to the creation of the microscope around 1595 and the telescope in 1608, both important tools for science.

Construction of simple lenses

Most lenses are spherical, meaning their two surfaces are parts of spheres. Each surface can be convex (bulging outwards), concave (depressed inward), or flat. The line joining the centers of these spheres is called the lens axis, which usually passes through the center of the lens.

Lenses are classified by the shape of their surfaces. A biconvex lens has both surfaces bulging outwards, while a biconcave lens has both surfaces curved inward. If one surface is flat, the lens is called plano-convex or plano-concave. Lenses with one convex and one concave surface are called meniscus lenses and are often used in eyeglasses to correct vision problems.

A biconvex or plano-convex lens in air focuses light to a point behind the lens and is called a converging lens. A biconcave or plano-concave lens spreads out light and is called a diverging lens. The distance from the lens to the focus point is known as the focal length.

Sign convention for Gaussian lens equation
Parameter	Meaning	+ Sign	− Sign
s_o	The distance between an object and a lens.	Real object	Virtual object
s_i	The distance between an image and a lens.	Real image	Virtual image
f	The focal length of a lens.	Converging lens	Diverging lens
y_o	The height of an object from the optical axis.	Erect object	Inverted object
y_i	The height of an image from the optical axis	Erect image	Inverted image
M_T	The transverse magnification in imaging ( = the ratio of y_i to y_o ).	Erect image	Inverted image

Imaging properties

A lens can focus light to a special point called the focal point. If a light source is placed at this focal point, the lens can make the light rays spread out evenly in all directions. These actions help create images.

Single thin lens imaging with chief rays

There are special rules that tell us where an image will form based on where the object is placed. For thin lenses, these rules can be shown with simple math. One key idea is that the distance from the object to the lens and the distance from the lens to the image are connected through the lens's focal length.

When an object is far away, the image forms at the focal point. If the object is close to the lens, the image can appear on the other side of the lens or even seem to be behind the lens, which we call a virtual image. Real images can be seen on screens, while virtual images can only be seen looking through the lens.

Images of Real Objects Formed by Thin Lenses
Lens Type	Object Location	Image Type	Image Location	Lateral Image Orientation	Image Magnification	Remark
Converging lens	∞ > S 1 > 2 f {\displaystyle \infty >S_{1}>2f}	Real	f	Inverted	Diminished
Converging lens	S 1 = 2 f {\displaystyle S_{1}=2f}	Real	S 2 = 2 f {\displaystyle S_{2}=2f}	Inverted	Same size
Converging lens	f	Real	∞ > S 2 > 2 f {\displaystyle \infty >S_{2}>2f}	Inverted	Magnified
Converging lens	S 1 = f {\displaystyle S_{1}=f}		± ∞ {\displaystyle \pm \infty }
Converging lens	S 1	Virtual	\| S 2 \| > S 1 {\displaystyle \vert S_{2}\vert >S_{1}}	Erect	Magnified	As an object moves toward the lens, the virtual image gets closer to the lens and the image size decreases.
Diverging lens	Anywhere	Virtual	\| S 2 \| \| S 2 \| {\displaystyle \vert S_{2}\vert \vert S_{2}\vert }	Erect	Diminished	As an object moves toward the lens, the virtual image gets closer to the lens and the image size increases.

Aberrations

Main article: Optical aberration

Lenses can’t make perfect images; they always cause some blurring or distortion, known as aberration. This happens because no lens is perfect, and different parts of the lens focus light differently. There are several common types of aberration that affect how clear an image looks.

Spherical aberration

Main article: Spherical aberration

Spherical aberration happens because lens shapes that are easy to make, like round curves, aren’t perfect for focusing light. Light beams far from the center of the lens focus in slightly different places than beams near the center, which can make images look blurry. Designers can reduce this problem by carefully choosing the curves of the lens for each use.

Coma

Main article: Coma (optics)

Coma makes images look like little comets. It happens when an object isn’t straight in front of the lens, and light rays pass through at an angle. Rays through the center of the lens focus in one place, while rays through the edges focus elsewhere, creating a flare-shaped blur. This can also be reduced by choosing the right curves for the lens.

Chromatic aberration

Main article: Chromatic aberration

Chromatic aberration occurs because a lens bends different colors of light by different amounts. This creates colorful edges around objects in an image. It can be lessened by combining two different types of glass in one lens, called an achromatic doublet, or by using special materials like fluorite, which bends light more evenly.

Other types of aberration

Other kinds of aberration include field curvature, barrel and pincushion distortion, and astigmatism.

Aperture diffraction

Even with perfect design, the way light spreads out when it passes through the lens opening, or aperture, can limit image quality. A diffraction-limited lens is one where this spreading of light is the main factor affecting the image.

Compound lenses

Simple lenses can create blurry images because of problems called optical aberrations. By combining two or more simple lenses into a compound lens, we can fix many of these problems. A compound lens is made of several simple lenses put together in a line, each made from materials that bend light slightly differently.

When light passes through several lenses one after another, each lens changes the shape of the light beam a little bit. The first lens makes an image, and that image becomes the object for the next lens, and so on, until the last lens creates the final image we see. This way, each lens helps improve the clarity and sharpness of the picture.

Non spherical types

Cylindrical lenses have curvature along only one direction and are used to focus light into a line or change the shape of light from a laser diode. Aspheric lenses have special shapes that help create clearer images than regular lenses.

Fresnel lenses are thin and light because their surface is split into narrow rings. Lenticular lenses are used in special printing to create images that change when you look at them from different angles. Other types of lenses, like bifocal lenses, have different focal lengths in different parts.

Uses

A watch with a plano-convex lens over the date indicator

Lenses are used in many everyday items to help us see better and capture images. For example, they are used in eyeglasses and contact lenses to correct vision problems like nearsightedness or farsightedness. They are also found in tools like magnifying glasses, binoculars, telescopes, microscopes, cameras, and projectors.

Lenses can also focus sunlight to a point strong enough to burn things, and they are used in special devices to collect energy for solar power. Some radio systems even use special lenses to help guide signals.