Definitions

# mirror

[mir-er]
mirror, in optics, a reflecting surface that forms an image of an object when light rays coming from that object fall upon it (see reflection). Usually mirrors are made of plate glass, one side of which is coated with metal or some special preparation to serve as a reflecting surface. The junction of this reflecting surface and the plate glass is called the mirror line. Highly polished metal and other materials serve also as mirrors; fused quartz is used for applications that require high precision because of its very low thermal expansion. Three common types of mirror are the plane mirror, which has a flat, or plane, surface; the convex mirror; and the concave mirror.

## The Plane Mirror

In a plane mirror the rays of light falling on it are reflected with little change in their original character and their relationship to one another in space. The apparent position of the image is the same distance behind the mirror as the actual object is in front of the mirror; the image is the same size as the object and is called a virtual image (i.e., the rays of light from the object do not actually go to the image, but extensions of the reflected light rays appear to intersect behind the mirror).

## Convex and Concave Mirrors

Convex and concave mirrors are known collectively as spherical mirrors, since their curved reflecting surfaces are usually part of the surface of a sphere. The concave type is one in which the midpoint or vertex of the reflecting surface is farther away from the object than are the edges. The center of the imaginary sphere of which it is a part is called the center of curvature and each point of the mirror surface is, therefore, equidistant from this point. A line extending through the center of curvature and the vertex of the mirror is the principal axis, and rays parallel to it are all reflected in such a way that they meet at a point on it lying halfway between the center of curvature and the vertex. This point is called the principal focus.

The size, nature, and position of an image formed by a concave spherical mirror depend on the position of the object in relation to the principal focus and the center of curvature. If the object is at a point farther from the mirror than the center of curvature, the image is real (i.e., it is formed directly by the reflected rays), inverted, and smaller than the object. If the object is at the center of curvature, the image is the same size as the object and is real and inverted. If the object is between the center of curvature and the principal focus, the image is larger, real, and inverted. If the object is inside the principal focus, the image is virtual, erect (right side up), and larger than the object. The position of the object can be found from the equation relating the focal length f of the mirror (the distance from the mirror to the principal focus), the distance do of the object from the mirror, and the distance di of the image from the mirror: 1/f=1/do+1/di. In the case of the virtual image, this equation yields a negative image distance, indicating that the image is behind the mirror. In the case of both the real and the virtual image, the size of the image is to the size of the object as the distance of the image from the mirror is to the distance of the object from the mirror.

In a convex spherical mirror the vertex of the mirror is nearer to the object than the edges—the mirror bulges toward the object. The image formed by it is always smaller than the object and always erect. It is never real because the reflected rays diverge outward from the face of the mirror and are not brought to a focus, and the image, therefore, is determined by their prolongation behind the mirror as in the case of the plane mirror.

## History and Development

The mirror of the ancient Greeks and Romans was a disk of metal with a highly polished face, sometimes with a design on the back, and usually with a handle. Glass mirrors date from the Middle Ages. They were made in large quantities in Venice from the 16th cent., the back being covered with a thin coating of tin mixed with mercury; after 1840 a thin coating of silver was generally substituted. The introduction of plate glass for mirrors (17th cent.) stimulated the use of large stationary mirrors as part of household furniture. Small bits of silvered glass were much used in the East to adorn articles of dress and of decoration. The metal trench hand mirror of World War I revived the manufacture of mirrors of this type. More recently, aluminum was introduced as the reflecting material because it is almost as efficient as silver but is more resistant to oxidation. Mirrors play an important part in the modern astronomical telescope.

A mirror is an object with a surface that has good specular reflection; that is, it is smooth enough to form an image. The most familiar type of mirror is the plane mirror, which has a flat surface. Curved mirrors are also used, to produce magnified or diminished images or focus light or simply distort the reflected image.

Mirrors are most commonly used for personal grooming (in which case the old-fashioned term "looking-glass" can be used), decoration, and architecture. Mirrors are also used in scientific apparatus such as telescopes and lasers, cameras, and industrial machinery. Most mirrors are designed for visible light; however, mirrors designed for other types of waves or other wavelengths of electromagnetic radiation are also used, especially in optical instruments.

## History

The earliest manufactured mirrors were pieces of polished stone such as obsidian, a naturally occurring volcanic glass. Examples of obsidian mirrors found in Anatolia (modern-day Turkey) have been dated to around 6000 BC. Polished stone mirrors from central and south America date from around 2000 BC onwards. Mirrors of polished copper were crafted in Mesopotamia from 4000 BC, and in ancient Egypt from around 3000 BC. In China, bronze mirrors were manufactured from around 2000 BC.

Metal-coated glass mirrors are said to have been invented in Sidon (modern-day Lebanon) in the first century AD, and glass mirrors backed with gold leaf are mentioned by the Roman author Pliny in his Natural History, written in about 77 AD. The Romans also developed a technique for creating crude mirrors by coating blown glass with molten lead.

Refracting parabolic mirrors were first described by the Arabian physicist, Ibn Sahl, in the 10th century, and was later described again by Ibn al-Haytham (Alhazen) in his famous Book of Optics (1021). Ibn al-Haytham discussed concave and convex mirrors in both cylindrical and spherical geometries, described spherical and parabolic mirrors, carried out a number of experiments with mirrors, and solved the problem of finding the point on a convex mirror at which a ray coming from one point is reflected to another point. By the 11th century, clear glass mirrors were being produced in Moorish Spain.

Some time during the early Renaissance, European manufacturers perfected a superior method of coating glass with a tin-mercury amalgam. The exact date and location of the discovery is unknown, but in the 16th century, Venice, a city famed for its glass-making expertise, became a centre of mirror production using this new technique. Glass mirrors from this period were extremely expensive luxuries. The Saint-Gobain factory, founded by royal initiative in France, was an important manufacturer, and Bohemian and German glass, often rather cheaper, was also important.

The invention of the silvered-glass mirror is credited to German chemist Justus von Liebig in 1835. His process involved the deposition of a thin layer of metallic silver onto glass through the chemical reduction of silver nitrate. This silvering process was adapted for mass manufacturing and led to the greater availability of affordable mirrors. Nowadays, mirrors are often produced by the vacuum deposition of aluminium (or sometimes silver) directly onto the glass substrate.

## Manufacturing

Most mirrors are made by applying a reflective coating to a suitable substrate. The most common such substrate is glass, due to its ease of fabrication, its rigidity, and its ability to take a smooth finish. The reflective coating is typically applied to the back surface of the glass, so that it is protected from corrosion and accidental damage. (Glass is much more scratch-resistant than most substrates.)

Historically, mirrors in the classical antiquity were made of solid metal (bronze, later silver) and they were too expensive for widespread use as well as being prone to corrosion. Due to polished metal's low reflectivity, antique mirrors also gave a darker picture compared to modern ones, making them unsuitable for indoor use with artificial lighting (candles or lanterns at the time).

The method of making mirrors out of ordinary glass was discovered by 16th century venetian glassmakers on the island of Murano, who covered the backside of plate glass with mercury, obtaining near-perfect reflection and imaging qualities. For over one hundred years venetian mirrors installed in richly decorated frames served as luxury decoration for palaces throughout Europe, but the secret of mercury process eventually arrived to London and Paris during the 17th century, due to industrial espionage. French workshops succeeded in large scale industrialization of the process, eventually making mirrors affordable to the masses, although mercury's toxicity remained a problem.

In modern times the mirror substrate is shaped, polished and cleaned, and is then coated. Glass mirrors are most often coated with non-toxic silver or aluminium, implemented by a series of coatings:

1. tin
2. silver
3. chemical activator
4. copper
5. paint

The tin is applied because silver will not bond with the glass. The activator causes the tin/silver to harden. Copper is added for long-term durability. The paint protects the coating on the back of the mirror from scratches and other accidental damage.

In some applications, generally those that are cost-sensitive or that require great durability, mirrors are instead made from a single, bulk material such as polished metal.

For technical applications such as laser mirrors, the reflective coating is typically applied by vacuum deposition on the front surface of the substrate. This eliminates double reflections and reduces absorption of light in the mirror. Cheaper technical mirrors use a silver, aluminium, or gold coating (the latter typically for infrared mirrors), and achieve reflectivities of 90–95% when new. A protective overcoat may be applied to prevent oxidation of the reflective layer. Applications requiring higher reflectivity or greater durability use dielectric coatings, which can achieve reflectivities as high as 99.999% over a narrow range of wavelengths.

## Effects

In a plane mirror, a parallel beam of light changes its direction as a whole, while still remaining parallel; the images formed by a plane mirror are virtual images, of the same size as the original object (see mirror image). There are also concave mirrors, where a parallel beam of light becomes a convergent beam, whose rays intersect in the focus of the mirror. Lastly, there are convex mirrors, where a parallel beam becomes divergent, with the rays appearing to diverge from a common intersection "behind" the mirror. Spherical concave and convex mirrors do not focus parallel rays to a single point due to spherical aberration. However, the ideal of focusing to a point is a commonly-used approximation. Parabolic reflectors resolve this, allowing incoming parallel rays (for example, light from a distant star) to be focused to a small spot; almost an ideal point. Parabolic reflectors are not suitable for imaging nearby objects because the light rays are not parallel.

A beam of light reflects off a mirror at an angle of reflection that is equal to its angle of incidence (if the size of a mirror is much larger than the wavelength of light). That is, if the beam of light is shining on a mirror's surface at a 30° angle from vertical, then it reflects from the point of incidence at a 30° angle from vertical in the opposite direction.

This law mathematically follows from the interference of a plane wave on a flat boundary (of much larger size than the wavelength).

## Applications

### Safety and easier viewing

Rear-view mirrors are widely used in and on vehicles (such as automobiles, or bicycles), to allow drivers to see other vehicles coming up behind them. Some motorcycle helmets have a built-in so-called MROS (Multiple Reflective Optic System): a set of reflective surfaces inside the helmet that together function as a rear-view mirror. There exist rear view sunglasses, of which the left end of the left glass and the right end of the right glass work as mirrors.

Convex mirrors are used to provide a wider field of view than a flat mirror. They are sometimes placed at road junctions, and corners of places such as parking lots to allow people to see around corners to avoid crashing into other vehicles or shopping carts. They are also sometimes used as part of security systems, so that a single video camera can show more than one angle at a time.

Mouth mirrors or "dental mirrors" are used by dentists to allow indirect vision and lighting within the mouth. Their reflective surfaces may be either flat or curved. Mouth mirrors are also commonly used by engineers to allow vision in tight spaces and around corners in equipment.

### Two-way mirrors

A two-way mirror, also sometimes referred to as a one-way mirror or one-way glass, reflects some percentage of the light and lets some other percentage pass. It is a sheet of glass coated with a layer of metal only a few dozen atoms thick, allowing some of the light through the surface (from both sides). It is used between a dark room and a brightly lit room. People on the brightly lit side see their own reflection — it looks like a normal mirror. People on the dark side see through it — it looks like a transparent window. It may be used to observe criminal suspects or customers. The same type of mirror, when used in an optical instrument, is called a half-silvered mirror or beam splitter. Its purpose is to split a beam of light so that half passes straight through, while the other half is reflected — this is useful for interferometry. The reality television program Big Brother makes extensive use of two-way mirrors throughout its set to allow cameramen in special black hallways to use movable cameras to videotape contestants without their coming in contact with the workers.

Contrary to popular belief, passive one-way mirrors that operate directionally between equally lit rooms do not exist. The laws of physics do not allow for real, passive one-way mirrors or windows (ones that do not need external energy); if such a device were possible, one could break the second law of thermodynamics and make energy flow from a cold object to a hot one, by placing such a mirror between them. One-way windows can be made to work with polarized light, however, without violating the second law. Optical isolators are one-way devices that are commonly used with lasers.

### Signalling

With the sun as light source, a mirror can be used to signal by variations in the orientation of the mirror. The signal can be used over long distances, possibly up to 60 kilometres on a clear day. This technique was used by Native American tribes and numerous militaries to transmit information between distant outposts.

Mirrors can also be used for rescue, especially to attract the attention of search and rescue helicopters. Specialised signalling mirrors are available and are often included in military survival kits.

### Technology

#### Televisions and projectors

Microscopic mirrors are a core element of many of the largest high-definition televisions and video projectors. A common technology of this type is Texas Instruments' DLP. A DLP chip is a postage stamp-sized microchip whose surface is comprised of an array of millions of microscopic mirrors. The picture is created as the individual mirrors move to either reflect light toward the projection surface (pixel on), or toward a light absorbing surface (pixel off).

Other projection technologies involving mirrors include LCoS. Like a DLP chip, LCoS is a microchip of similar size, but rather than millions of individual mirrors, there is a single mirror that is actively shielded by a liquid crystal matrix with up to millions of pixels. The picture is formed as light is either reflected toward the projection surface (pixel on), or absorbed by the activated LCD pixels (pixel off). LCoS-based televisions and projectors often use 3 chips, one for each primary color.

Large mirrors are used in rear projection televisions. Light (for example from a DLP as mentioned above) is "folded" by one or more mirrors so that the television set is compact.

#### Instruments

Telescopes and other precision instruments use front silvered or first surface mirrors, where the reflecting surface is placed on the front (or first) surface of the glass (this eliminates reflection from glass surface ordinary back mirrors have). Some of them use silver, but most are aluminum, which is more reflective at short wavelengths than silver. All of these coatings are easily damaged and require special handling. They reflect 90% to 95% of the incident light when new. The coatings are typically applied by vacuum deposition. A protective overcoat is usually applied before the mirror is removed from the vacuum, because the coating otherwise begins to corrode as soon as it is exposed to oxygen and humidity in the air. Front silvered mirrors have to be resurfaced occasionally to keep their quality.

The reflectivity of the mirror coating can be measured using a reflectometer and for a particular metal it will be different for different wavelengths of light. This is exploited in some optical work to make cold mirrors and hot mirrors. A cold mirror is made by using a transparent substrate and choosing a coating material that is more reflective to visible light and more transmissive to infrared light. A hot mirror is the opposite, the coating preferentially reflects infrared. Mirror surfaces are sometimes given thin film overcoatings both to retard degradation of the surface and to increase their reflectivity in parts of the spectrum where they will be used. For instance, aluminum mirrors are commonly coated with silicon dioxide or magnesium fluoride. The reflectivity as a function of wavelength depends on both the thickness of the coating and on how it is applied.

For scientific optical work, dielectric mirrors are often used. These are glass (or sometimes other material) substrates on which one or more layers of dielectric material are deposited, to form an optical coating. By careful choice of the type and thickness of the dielectric layers, the range of wavelengths and amount of light reflected from the mirror can be specified. The best mirrors of this type can reflect >99.999% of the light (in a narrow range of wavelengths) which is incident on the mirror. Such mirrors are often used in lasers.

In astronomy, adaptive optics is a technique to measure variable image distortions and adapt a deformable mirror accordingly on a timescale of milliseconds, to compensate for the distortions.

Although the most of mirrors are designed to reflect visible light, surfaces reflecting other forms of electromagnetic radiation are also called "mirrors". The mirrors for other ranges of electromagnetic waves are used in optics and astronomy. Mirrors for radio waves are important elements of radio telescopes.

A Mangin mirror is a combination lens and concave mirror and is widely used in optical instruments and even sometimes in cameras.

##### Face-to-face mirrors

Some devices use two or more mirrors facing one another to generate multiple reflections:

The reflected images between these mirrors give the appearance of an infinite regress.

#### Military applications

It has been said that Archimedes used a large array of mirrors to burn Roman ships during an attack on Syracuse. This has never been proven or disproved; however, many have put it to the test. Recently, on a popular Discovery Channel show, MythBusters, a team from MIT tried to recreate the famous "Archimedes Death Ray". They were successful at starting a fire on a ship at 75 feet away; however, previous attempts to light the boat on fire using only the bronze mirrors available in Archimedes' time were unsuccessful, and the time taken to ignite the craft would have made its use impractical, resulting in the MythBusters team deeming the myth "busted". (However, see solar power tower for a practical use of this technique.)

#### Seasonal lighting

Due to its location in a steep-sided valley, the Italian town of Viganella gets no direct sunlight for seven weeks each winter. In 2006 a €100,000 computer-controlled mirror, 8×5 m, was installed to reflect sunlight into the town's piazza. In early 2007 the similarly situated village of Bondo, Switzerland, was considering applying this solution as well. Mirrors can be used to produce enhanced lighting effects in greenhouses or conservatories.

### Leisure

#### Decoration

Mirrors, typically large and unframed, are frequently used in interior decoration to create an illusion of space, and amplify the apparent size of a room.

Mirrors are used also in some schools of feng shui, an ancient Chinese practice of placement and arrangement of space to achieve harmony with the environment.

The softness of old mirrors is sometimes replicated by contemporary artisans for use in interior design. These reproduction antiqued mirrors are works of art and can bring color and texture to an otherwise hard, cold reflective surface. It is an artistic process that has been attempted by many and perfected by few.

A decorative reflecting sphere of thin metal-coated glass, working as a reducing wide-angle mirror, is sold as a Christmas ornament called a bauble.

#### Entertainment

The hall of mirrors, commonly found in amusement parks, is an attraction in which a number of distorted mirrors are used to produce unusual reflections of the visitor. Mirror mazes, also found in amusement parks, contain large numbers of mirrors and sheets of glass. The idea is to navigate the disorientating array without bumping into the walls.

Mirrors are often used in magic to create an illusion. One effect is called Pepper's ghost. Illuminated rotating disco balls covered with small mirrors are used to cast moving spots of light around a dance floor. Mirrors are employed in kaleidoscopes, personal entertainment devices invented in Scotland by sir David Brewster.

#### Art

Filippo Brunelleschi discovered linear perspective with the help of the mirror, Leonardo da Vinci called the mirror the "master of painters". He recommended. "When you wish to see whether your whole picture accords with what you have portrayed from nature take a mirror and reflect the actual object in it. Compare what is reflected with your painting and carefully consider whether both likenesses of the subject correspond, particularly in regard to the mirror. The mirror is the central device in some of the greatest of European paintings: Jan Van Eyck's Arnolfini Portrait, Diego Velazquez's Las Meninas and Edouard Manet’s A Bar at the Folies-Bergère. Without a mirror, the great self portraits by Dürer, Rembrandt, Van Gogh and Frida Kahlo could not have been painted. M. C. Escher used special shapes of mirrors in order to have a much more complete view of the surroundings than by direct observation (Hand with Reflecting Sphere). István Orosz’s anamorphic works are images distorted such way that they only become clearly visible when reflected in a suitably-shaped and positioned mirror. Some other contemporary artists use mirrors as the material of art, like in mirror-sculptures and paintings on mirror surfaces. Some artists build special mirror installations as the neon mirror cubes by Jeppe Hein.

Painters depicting someone in front of a mirror often also show the person's reflection. This is a kind of abstraction—in most cases the angle of view is such that the person's reflection should not be visible. Similarly, in movies and still photography an actor or actress is often shown ostensibly looking at him or herself in the mirror, and yet the reflection faces the camera. In reality, the actor or actress sees only the camera and its operator in this case, not their own reflection.

#### Literature

Mirrors play a powerful role in cultural literature, from the self-loving Narcissus of Greek Mythology to the Biblical reference to Through a Glass Darkly. The evil queen in the European fairy-tale Snow White asked, "Mirror, mirror, on the wall... who's the fairest of them all?" Some of the best-loved uses of mirrors in literature include Lewis Carroll's Alice's Adventures in Wonderland and the Mirror of Erised in the Harry Potter series. Horror movies about mirrors include Candyman and Mirrors.

## Mirrors and superstition

There are many legends and superstitions surrounding mirrors. Mirrors are said to be a reflection of the soul, and they were often used in traditional witchcraft as tools for scrying or performing other spells. It is also said that mirrors cannot lie. They can show only the truth, so it is a very bad omen indeed to see something in a mirror which should not be there.

It is a common superstition that someone who breaks a mirror will receive seven years of bad luck. One of the many reasons for this belief is that the mirror is believed to reflect part of the soul, therefore, breaking the mirror will break part of the soul. However, the soul is said to regenerate every seven years, thus coming back unbroken. To counter this one of many rituals has to be performed, the easiest of which is to stop the mirror from reflecting the broken soul by grinding it to dust. The belief might also simply originate from the high cost of mirrors in times gone past.

In days past it was customary in the southern United States to cover the mirrors in a house where the wake of a deceased person was being held. It was believed that the person's soul would become trapped in a mirror left uncovered. Mirrors falling from walls or otherwise breaking or cracking mysteriously were said to be haunted.

According to legend, a vampire has no reflection in mirrors because it is an undead creature and has already lost its soul.

Another superstition claims it is bad luck to have two mirrors facing each other.

A staple of childhood slumber parties is the game Bloody Mary (folklore), which involves chanting "Bloody Mary" three times in a darkened room while staring into a mirror. There are many versions of the game, but the general idea is that "Mary" will appear in the mirror and attempt to harm or kill the person who has summoned her. Thanks to a series of popular horror movies based on a supernatural killer who haunted mirrors, the phrase "Candy Man" may be substituted for Mary.

## Mirrors and animals

Experiments have shown that only large-brained social animals are able to recognise that a mirror shows a reflection of themselves.

Animals that have shown they are able to use a mirror to study themselves:

## Unusual types of mirror

Other types of reflecting device are also called "mirrors". For example metallic reflectors are used to reflect infrared light (such as in space heaters), or microwaves.

An acoustic mirror is a passive device used to reflect and perhaps to focus sound waves. Acoustic mirrors were used for selective detection of sound waves, especially during World War 2. They were used for detection of enemy aircraft prior to the development of radar. Acoustic mirrors are used for remote probing of the atmosphere; they can be used to form a narrow diffraction-limited beam. They can also be used for underwater "imaging".

Active mirrors are mirrors that amplify the light they reflect. They are used to make disk lasers. The amplification is typically over a narrow range of wavelengths, and requires an external source of power.

An atomic mirror is a device which reflects matter waves. Usually, atomic mirrors work at grazing incidence. Such a mirror can be used for atomic interferometry and atomic holography. It has been proposed that they can be used for non-destructive imaging systems with nanometer resolution.

Cold mirrors are dielectric mirrors that reflect the entire visible light spectrum while efficiently transmitting infrared wavelengths. Conversely, hot mirrors reflect infrared light while allowing visible light to pass. These can be used to separate useful light from unneeded infrared to reduce heating of components in an optical device. They can also be used as dichroic beamsplitters.

Corner reflectors use three flat mirrors to reflect light back towards its source. They are used for emergency location, and even laser ranging to the Moon.

X-ray mirrors produce specular reflection of X-rays. All known types work only at angles near grazing incidence, and only a small fraction of the rays are reflected.

## Bibliography

• Mirror, Mirror: A History of the Human Love Affair with Reflection, Mark Pendergrast. Basic Books (2003). ISBN 0-465-05471-4 .
• On reflection, Jonathan Miller, National Gallery Publications Limited (1998). ISBN 0-300-07713-0 .
• The Mirror: A History, Sabine Melchior-Bonnet, Routledge, 2001, ISBN 0415924480