Editing Mirror (section)

==Physical principles==
[[File:Mirror reflecting light waves.png|thumb|A mirror reflects light waves to the observer, preserving the wave's curvature and divergence, to form an image when focused through the lens of the eye. The angle of the impinging wave, as it traverses the mirror's surface, matches the angle of the reflected wave.]]
When a sufficiently narrow beam of light is reflected at a point of a surface, the [[surface normal|surface's normal direction]] <math>\vec n</math> will be the bisector of the angle formed by the two beams at that point. That is, the [[direction vector]] <math>\vec u</math> towards the incident beams's source, the normal vector <math>\vec n</math>, and direction vector <math>\vec v</math> of the reflected beam will be [[coplanarity|coplanar]], and the angle between <math>\vec n</math> and <math>\vec v</math> will be equal to the [[angle of incidence (optics)|angle of incidence]] between <math>\vec n</math> and <math>\vec u</math>, but of opposite sign.<ref name=katz2016/>

This property can be explained by the physics of an [[electromagnetic wave|electromagnetic]] [[plane wave]] that is incident to a flat surface that is [[electrical conductance|electrically conductive]] or where the [[speed of light]] changes abruptly, as between two materials with different indices of refraction.

* When [[parallel (geometry)|parallel]] beams of light are reflected on a plane surface, the reflected rays will be parallel too.
* If the reflecting surface is concave, the reflected beams will be [[Vergence (optics)|convergent]], at least to some extent and for some distance from the surface.
* A convex mirror, on the other hand, will reflect parallel rays towards [[divergence|divergent]] directions.

More specifically, a concave parabolic mirror (whose surface is a part of a paraboloid of revolution) will reflect rays that are parallel to its [[surface of revolution|axis]] into rays that pass through its [[focus (optics)|focus]]. Conversely, a parabolic concave mirror will reflect any ray that comes from its focus towards a direction parallel to its axis. If a concave mirror surface is a part of a [[ellipsoid|prolate ellipsoid]], it will reflect any ray coming from one focus toward the other focus.<ref name=katz2016/>

A convex parabolic mirror, on the other hand, will reflect rays that are parallel to its axis into rays that seem to emanate from the focus of the surface, behind the mirror. Conversely, it will reflect incoming rays that converge toward that point into rays that are parallel to the axis. A convex mirror that is part of a prolate ellipsoid will reflect rays that converge towards one focus into divergent rays that seem to emanate from the other focus.<ref name=katz2016/>

Spherical mirrors do not reflect parallel rays to rays that converge to or diverge from a single point, or vice versa, due to [[spherical aberration]]. However, a spherical mirror whose diameter is sufficiently small compared to the sphere's radius will behave very similarly to a parabolic mirror whose axis goes through the mirror's center and the center of that sphere; so that spherical mirrors can substitute for parabolic ones in many applications.<ref name=katz2016/>

A similar aberration occurs with parabolic mirrors when the incident rays are parallel among themselves but not parallel to the mirror's axis, or are divergent from a point that is not the focus – as when trying to form an image of an object that is near the mirror or spans a wide angle as seen from it. However, this aberration can be sufficiently small if the object image is sufficiently far from the mirror and spans a sufficiently small angle around its axis.<ref name=katz2016/>

===Mirror images===
{{Main|Mirror image}}
[[File:Lake O Hara Early Morning Reflection (173874897).jpeg|thumb|A mirror reverses an image in the direction of the normal [[Angle of incidence (optics)|angle of incidence]]. When the surface is at a 90°, horizontal angle from the object, the image appears inverted 180° along the vertical (right and left remain on the correct sides, but the image appears upside down), because the normal angle of incidence points down vertically toward the water.]]
[[File:Mirror virtual image.png|thumb|A mirror reflects a real image (blue) back to the observer (red), forming a virtual image; a perceptual illusion that objects in the image are behind the mirror's surface and facing the opposite direction (purple). The arrows indicate the direction of the real and perceived images, and the reversal is analogous to viewing a movie with the film facing backwards, except the "screen" is the viewer's retina.]]

Mirrors reflect an image to the observer. However, unlike a projected image on a screen, an image does not actually exist on the surface of the mirror. For example, when two people look at each other in a mirror, both see different images on the same surface. When the light waves converge through the lens of the eye they interfere with each other to form the image on the surface of the [[retina]], and since both viewers see waves coming from different directions, each sees a different image in the same mirror. Thus, the images observed in a mirror depend upon the angle of the mirror with respect to the eye. The angle between the object and the observer is always twice the angle between the eye and the normal, or the direction perpendicular to the surface. This allows animals with [[binocular vision]] to see the reflected image with [[depth perception]] and in three dimensions.

The mirror forms a ''virtual image'' of whatever is in the opposite angle from the viewer, meaning that objects in the image appear to exist in a direct [[line of sight]]—behind the surface of the mirror—at an equal distance from their position in front of the mirror. Objects behind the observer, or between the observer and the mirror, are reflected back to the observer without any actual change in orientation; the light waves are simply reversed in a direction perpendicular to the mirror. However, when viewer is facing the object and the mirror is at an angle between them, the image appears inverted 180° along the direction of the angle.<ref name="ReferenceA">''Mastering Physics for ITT-JEE, Volume 2'' By S. Chand & Co. 2012 Er. Rakesh Rathi Page 273--276</ref>

Objects viewed in a (plane) mirror will appear laterally inverted (e.g., if one raises one's right hand, the image's left hand will appear to go up in the mirror), but not vertically inverted (in the image a person's head still appears above their body).<ref name=lard1845/> However, a mirror does not actually "swap" left and right any more than it swaps top and bottom. A mirror swaps front and back. To be precise, it reverses the object in the direction perpendicular to the mirror surface (the normal), turning the three dimensional image inside out (the way a glove stripped off the hand can be turned inside out, turning a left-hand glove into a right-hand glove or vice versa). When a person raises their left hand, the actual left hand raises in the mirror, but gives the illusion of a right hand raising because the imaginary person in the mirror is literally inside-out, hand and all. If the person stands side-on to a mirror, the mirror really does reverse left and right hands, that is, objects that are physically closer to the mirror always appear closer in the virtual image, and objects farther from the surface always appear symmetrically farther away regardless of angle.

Looking at an image of oneself with the front-back axis flipped results in the perception of an image with its left-right axis flipped. When reflected in the mirror, a person's right hand remains directly opposite their real right hand, but it is perceived by the mind as the left hand in the image. When a person looks into a mirror, the image is actually front-back reversed (inside-out), which is an effect similar to the [[hollow-mask illusion]]. Notice that a mirror image is fundamentally different from the object (inside-out) and cannot be reproduced by simply rotating the object. An object and its mirror image are said to be [[chiral]].

For things that may be considered as two-dimensional objects (like text), front-back reversal cannot usually explain the observed reversal. An image is a two-dimensional representation of a three-dimensional space, and because it exists in a two-dimensional [[Focal plane|plane]], an image can be viewed from front or back. In the same way that text on a piece of paper appears reversed if held up to a light and viewed from behind, text held facing a mirror will appear reversed, because the image of the text is still facing away from the observer. Another way to understand the reversals observed in images of objects that are effectively two-dimensional is that the inversion of left and right in a mirror is due to the way human beings perceive their surroundings. A person's reflection in a mirror appears to be a real person facing them, but for that person to really face themselves (i.e.: twins) one would have to physically turn and face the other, causing an actual swapping of right and left. A mirror causes an illusion of left-right reversal because left and right were ''not'' swapped when the image appears to have turned around to face the viewer. The viewer's [[egocentric navigation]] (left and right with respect to the observer's point of view; i.e.: "my left...") is unconsciously replaced with their [[allocentric navigation]] (left and right as it relates another's point of view; "...your right") when processing the virtual image of the apparent person behind the mirror. Likewise, text viewed in a mirror would have to be physically turned around, facing the observer and away from the surface, actually swapping left and right, to be read in the mirror.<ref name="ReferenceA"/>