Mirror image

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In geometry, the mirror image of an object or two-dimensional figure is the virtual image formed by reflection in a plane mirror; it is of the same size as the original object, yet different, unless the object or figure has reflection symmetry (also known in the terminology of modern physics as a P-symmetry).

Examples:

  • The mirror-image of b is d or p (d and p are equal except for orientation).
  • The tetrominos S and Z

The concept of mirror image can be extended to three-dimensional objects, including the inside parts, even if they are not transparent. The term then relates to structural as well as visual aspects. This is also called enantiomer or enantiomorph.

Chirality is a term in geometry where a figure is said to be chiral if it is not identical to its mirror image, or, more precisely, can't be mapped to its mirror image by rotations and translations alone.

Examples:

  • The mirror-image of a right hand is like a left hand.
  • The mirror-image of a human body is roughly like a human body, but with internal differences; for a particular person there are also minor external differences, the most striking may be the hair if that is not symmetrically cut and combed.
  • The 3D tetrominos left and right screw
  • The two versions of the snub cube are mirror images of each other.
  • The two isomers in the case of optical isomerism.
  • Clothing is often approximately symmetric. However, for fastening the right to the left side (of a shirt, coat, flies, dress, etc.), often on the front side, but also on the back side, if buttons are used one side goes over the other; in the case of a zip fastener there is at least minor asymmetry, but often also one flap goes over the other. A belt, although often vertically symmetric, provides also asymmetry. A skirt may have a zip fastener on one side. There may also be asymmetry with regard to pockets, for example only one inner pocket.

A mirror image of a two-dimensional figure is also obtained when looking at it from the other side, in the case that the figure can still be seen from there. This may be the case due to transparency, or if the coloring is not just at the surface but through and through.

Examples:

  • text or pictures on glass or textiles (a printed T-shirt worn inside out, a parasol)
  • paper printed on one side, looked at from the other side, holding it to the light

The mirror-image of a mirror image is a regular image. When you see a reflection that surprisingly is a regular image this is usually caused by the fact that you are looking at the reflection of a reflection, or the reflection of an image seen from the other side (see above). On sunny days perhaps the most common example of the latter is seeing the reflection in a window of the inside of a parasol with text on it.

Occasionally you can see a mirror image, even though you are aware of looking at the reflection of a reflection; this may be due to a third reflection.

A text is sometimes deliberately displayed in mirror image, in order to be read through a mirror, e.g:

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.

In the case of two mirrors, say vertical ones, 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 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, 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.

A special kind of "mirror image" of a text is with the letters in reversed order, while the individual letters are normal, see http://wikipedia.org.mirror.sytes.org/wiki/mirror_image and elgooG. The real mirror image of that is with the letters in normal order, but each in mirror image.

See also

nl:Spiegelbeeld