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A mirror image (in a plane mirror) is a reflected duplication of an object that appears almost identical, but is reversed in the direction perpendicular to the mirror surface. As an
optical Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultravio ...
effect it results from
reflection Reflection or reflexion may refer to: Science and technology * Reflection (physics), a common wave phenomenon ** Specular reflection, reflection from a smooth surface *** Mirror image, a reflection in a mirror or in water ** Signal reflection, in ...
off from substances such as a
mirror A mirror or looking glass is an object that reflects an image. Light that bounces off a mirror will show an image of whatever is in front of it, when focused through the lens of the eye or a camera. Mirrors reverse the direction of the im ...
or
water Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as ...
. It is also a concept in
geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
and can be used as a conceptualization process for 3-D structures.


In geometry and geometrical optics


In two dimensions

In
geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
, the mirror image of an object or two-dimensional figure is the
virtual image In optics, an ''image'' is defined as the collection of focus points of light rays coming from an object. A '' real image'' is the collection of focus points made by converging rays, while a virtual image is the collection of focus points ma ...
formed by
reflection Reflection or reflexion may refer to: Science and technology * Reflection (physics), a common wave phenomenon ** Specular reflection, reflection from a smooth surface *** Mirror image, a reflection in a mirror or in water ** Signal reflection, in ...
in a
plane mirror A plane mirror is a mirror with a flat ( planar) reflective surface. For light rays striking a plane mirror, the angle of reflection equals the angle of incidence. The angle of the incidence is the angle between the incident ray and the surfac ...
; it is of the same size as the original object, yet different, unless the object or figure has
reflection symmetry In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry. In 2D the ...
(also known as a
P-symmetry In physics, a parity transformation (also called parity inversion) is the flip in the sign of ''one'' spatial coordinate. In three dimensions, it can also refer to the simultaneous flip in the sign of all three spatial coordinates (a point refle ...
). Two-dimensional mirror images can be seen in the reflections of mirrors or other reflecting surfaces, or on a printed surface seen inside-out. If we first look at an object that is effectively two-dimensional (such as the writing on a card) and then turn the card to face a mirror, the object turns through an angle of 180° and we see a left-right reversal in the mirror. In this example, it is the change in orientation rather than the mirror itself that causes the observed reversal. Another example is when we stand with our backs to the mirror and face an object that's in front of the mirror. Then we compare the object with its reflection by turning ourselves 180°, towards the mirror. Again we perceive a left-right reversal due to a change in our orientation. So, in these examples the mirror does not actually cause the observed reversals.


In three dimensions

The concept of reflection can be extended to
three-dimensional Three-dimensional space (also: 3D space, 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called '' parameters'') are required to determine the position of an element (i.e., point). This is the inform ...
objects, including the inside parts, even if they are not
transparent Transparency, transparence or transparent most often refer to: * Transparency (optics), the physical property of allowing the transmission of light through a material They may also refer to: Literal uses * Transparency (photography), a still, ...
. The term then relates to structural as well as visual aspects. A three-dimensional object is reversed in the direction perpendicular to the mirror surface. In physics, mirror images are investigated in the subject called
geometrical optics Geometrical optics, or ray optics, is a model of optics that describes light propagation in terms of '' rays''. The ray in geometrical optics is an abstraction useful for approximating the paths along which light propagates under certain circumstan ...
. More fundamentally in geometry and mathematics they form the principal objects of
Coxeter group In mathematics, a Coxeter group, named after H. S. M. Coxeter, is an abstract group that admits a formal description in terms of reflections (or kaleidoscopic mirrors). Indeed, the finite Coxeter groups are precisely the finite Euclidean refle ...
theory and
reflection group In group theory and geometry, a reflection group is a discrete group which is generated by a set of reflections of a finite-dimensional Euclidean space. The symmetry group of a regular polytope or of a tiling of the Euclidean space by congruent c ...
s. In chemistry, two versions (isomers) of a molecule, one a "mirror image" of the other, are called
enantiomer In chemistry, an enantiomer ( /ɪˈnænti.əmər, ɛ-, -oʊ-/ ''ih-NAN-tee-ə-mər''; from Ancient Greek ἐνάντιος ''(enántios)'' 'opposite', and μέρος ''(méros)'' 'part') – also called optical isomer, antipode, or optical anti ...
s if they are not "superposable" (the correct technical term, though the term "superimposable" is also used) on each other. That is an example of
chirality (chemistry) In chemistry, a molecule or ion is called chiral () if it cannot be superposed on its mirror image by any combination of rotations, translations, and some conformational changes. This geometric property is called chirality (). The terms a ...
. In general, an object and its mirror image are called enantiomorphs. If a point of an object has coordinates (''x'', ''y'', ''z'') then the image of this point (as reflected by a mirror in the ''y'', ''z'' plane) has coordinates (−''x'', ''y'', ''z''). Thus reflection is a reversal of the coordinate axis perpendicular (
normal Normal(s) or The Normal(s) may refer to: Film and television * ''Normal'' (2003 film), starring Jessica Lange and Tom Wilkinson * ''Normal'' (2007 film), starring Carrie-Anne Moss, Kevin Zegers, Callum Keith Rennie, and Andrew Airlie * ''Norma ...
) to the mirror's surface. Although a plane mirror reverses an object only in the direction normal to the mirror surface, this turns the entire three-dimensional image seen in the mirror inside-out, so there is a ''perception'' of a left-right reversal. Hence, the reversal is somewhat misleadingly called a "lateral inversion". The perception of a left-right reversal is geometrically explained by the fact that a three-dimensional object seen in a mirror is an inside-out version of the actual object, like a glove stripped off the left hand and turned into a right-hand glove, but there is still some confusion about the explanation amongst psychologists. The psychology of the perceived left-right reversal is discussed in "Much ado about mirrors" by Professor
Michael Corballis Michael Charles Corballis (10 September 1936 – 13 November 2021) was a New Zealand and Canadian psychologist and author. He was Emeritus Professor at the Department of Psychology at the University of Auckland. His fields of research were ...
(see "external links", below). Reflection in a mirror ''does'' result in a change in
chirality Chirality is a property of asymmetry important in several branches of science. The word ''chirality'' is derived from the Greek (''kheir''), "hand", a familiar chiral object. An object or a system is ''chiral'' if it is distinguishable from ...
, more specifically from a right-handed to a left-handed coordinate system (or vice versa). If one looks in a mirror two axes (up-down and left-right) coincide with those in the mirror, but the third axis (front-back) is reversed. If a person stands side-on to a mirror, left and right hands will be reversed ''directly'' by the mirror, because the person's left-right axis is then normal to the mirror plane. However, it's important to understand that there are ''always'' only two enantiomorphs, the object and its inside-out image. Therefore, no matter how the object is oriented towards the mirror, all the resulting images are fundamentally identical (as Corballis explains in his paper "Much ado about mirrors", mentioned above). In the picture of the mountain reflected in the lake (photograph top right), the reversal normal to the reflecting surface is obvious. Notice that there is no obvious front-back or left-right of the mountain. In the example of the urn and mirror (photograph to right), the urn is fairly symmetrical front-back (and left-right). Thus, no obvious reversal of any sort can be seen in the mirror image of the urn. A mirror image appears more obviously three-dimensional if the observer moves, or if the image is viewed using
binocular vision In biology, binocular vision is a type of vision in which an animal has two eyes capable of facing the same direction to perceive a single three-dimensional image of its surroundings. Binocular vision does not typically refer to vision where an ...
. This is because the relative position of objects changes as the observer's perspective changes, or is differently viewed with each eye. Looking through a mirror from different positions (but necessarily with the point of observation restricted to the halfspace on one side of the mirror) is like looking at the 3D mirror image of space; without further mirrors only the mirror image of the halfspace before the mirror is relevant; if there is another mirror, the mirror image of the other halfspace is too.


Effect of mirror on the lighting of the scene

A mirror does not just produce an image of what would be there without it; it also changes the light distribution in the halfspace in front of and behind the mirror. A mirror hanging on the wall makes the room brighter because additional light sources appear in the mirror image. However, the appearance of additional light does not violate the
conservation of energy In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be ''conserved'' over time. This law, first proposed and tested by Émilie du Châtelet, means tha ...
principle, because some light no longer reaches behind the mirror, as the mirror simply re-directs the light energy. In terms of the light distribution, the virtual mirror image has the same appearance and the same effect as a real, symmetrically arranged half-space behind a window (instead of the mirror). Shadows may extend from the mirror into the halfspace before it, and vice versa.


Mirror writing

In
mirror writing Mirror writing is formed by writing in the direction that is the reverse of the natural way for a given language, such that the result is the mirror image of normal writing: it appears normal when it is reflected in a mirror. It is sometimes u ...
a text is deliberately displayed as its mirror image, in order to be read through a mirror. For example, emergency vehicles such as
ambulance An ambulance is a medically equipped vehicle which transports patients to treatment facilities, such as hospitals. Typically, out-of-hospital medical care is provided to the patient during the transport. Ambulances are used to respond to med ...
s or fire engines use mirror images in order to be read from a vehicle's
rear-view mirror A rear-view mirror (or rearview mirror) is a flat mirror in automobiles and other vehicles, designed to allow the driver to see rearward through the vehicle's rear window (rear windshield). In cars, the rear-view mirror is usually affixed to ...
. Some
movie theater A movie theater (American English), cinema (British English), or cinema hall ( Indian English), also known as a movie house, picture house, the movies, the pictures, picture theater, the silver screen, the big screen, or simply theater is a ...
s also use mirror writing in a Rear Window Captioning System used to assist individuals with
hearing impairment Hearing loss is a partial or total inability to hear. Hearing loss may be present at birth or acquired at any time afterwards. Hearing loss may occur in one or both ears. In children, hearing problems can affect the ability to acquire spoken la ...
s in watching films.


Systems of mirrors

In the case of two mirrors, in planes at an angle α, looking through both from the sector which is the intersection of the two halfspaces, is like looking at a version of the world rotated by an angle of 2α; the points of observations and directions of looking for which this applies correspond to those for looking through a frame like that of the first mirror, and a frame at the mirror image with respect to the first plane, of the second mirror. If the mirrors have vertical edges then the left edge of the field of view is the plane through the right edge of the first mirror and the edge of the second mirror which is on the right when looked at directly, but on the left in the mirror image. In the case of two parallel mirrors, looking through both at once is like looking at a version of the world which is translated by twice the distance between the mirrors, in the direction perpendicular to them, away from the observer. Since the plane of the mirror in which one looks directly is beyond that of the other mirror, one always looks at an oblique angle, and the translation just mentioned has not only a component away from the observer, but also one in a perpendicular direction. The translated view can also be described by a translation of the observer in opposite direction. For example, with a vertical
periscope A periscope is an instrument for observation over, around or through an object, obstacle or condition that prevents direct line-of-sight observation from an observer's current position. In its simplest form, it consists of an outer case with ...
, the shift of the world is away from the observer and down, both by the length of the periscope, but it is more practical to consider the equivalent shift of the observer: up, and backward. It is also possible to create a
non-reversing mirror A non-reversing mirror (sometimes referred to as a flip mirror) is a mirror that presents its subject as it would be seen from the mirror. A non-reversing mirror can be made by connecting two regular mirrors at their edges at a 90 Degree (angle) ...
by placing two first surface mirrors at 90º to give an image which is not reversed.


See also

*
Anamorphosis Anamorphosis is a distorted projection requiring the viewer to occupy a specific vantage point, use special devices, or both to view a recognizable image. It is used in painting, photography, sculpture and installation, toys, and film special e ...
*
Chirality Chirality is a property of asymmetry important in several branches of science. The word ''chirality'' is derived from the Greek (''kheir''), "hand", a familiar chiral object. An object or a system is ''chiral'' if it is distinguishable from ...
, a property of asymmetry important in several branches of science *
Flipped image A flipped image or reversed image, the more formal term, is a static or moving image that is generated by a mirror-reversal of an original across a horizontal axis (a '' flopped'' image is mirrored across the vertical axis).Ron Brinkmann"The Art ...
*
Flopped image In photography and graphic arts a flopped image is a technical term for a static or moving image that is generated by a mirror-reversal of an original image across a vertical axis. This is opposed to a ''flipped image'', which means an image rev ...
*
Handedness In human biology, handedness is an individual's preferential use of one hand, known as the dominant hand, due to it being stronger, faster or more dextrous. The other hand, comparatively often the weaker, less dextrous or simply less subject ...
* Infinity mirror *
Kaleidoscope A kaleidoscope () is an optical instrument with two or more reflecting surfaces (or mirrors) tilted to each other at an angle, so that one or more (parts of) objects on one end of these mirrors are shown as a regular symmetrical pattern when v ...
*
Plane mirror A plane mirror is a mirror with a flat ( planar) reflective surface. For light rays striking a plane mirror, the angle of reflection equals the angle of incidence. The angle of the incidence is the angle between the incident ray and the surfac ...
*
Reflection (physics) Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. Th ...
*
Relative direction In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents the position of a point ''P'' in space in relation to an arbitrary reference origin ''O''. Usually denoted x, r, or ...


References


External links

{{Commons category, Mirroring
Why do mirrors reverse images left to right? Why not up and down?


* ttps://www.youtube.com/watch?v=vBpxhfBlVLU Why do mirrors flip horizontally (but not vertically)?
"Much ado about mirrors" (an academic paper about the psychology involved in the perception of mirror images)
Elementary geometry Chirality Counterparts