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the mirror image of an object or two-dimensional figure
Publisher:admin  12-05-16  Click:4  
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In two dimensionsIn 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 as a P-symmetry).

Two-dimensional mirror images can be seen in the reflections of mirrors or other reflecting surfaces, or on a printed surface seen inside out.

[edit] In three dimensionsThe 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.

If a point of an object has coordinates (x, y,z) then the image of this point (as reflected from the mirror in y, z plane) has coordinates (-x, y,z) - so mirror reflection is a reversal of the coordinate axis perpendicular to the mirror's surface. Thus, a mirror image does not have reversed right and left (or up and down), but rather reversed front and back. The left-right reversal of the mirror image only holds in relation a normal (i.e. unreflected) picture that we see in front of us; see schematic illustration at the right. For instance, if we look at a picture or object in our hand and then turn it towards a mirror, the picture and thus its mirror reflection have made a left-to-right 'flip over' of 180 degrees. The same principle holds when we stand with our back towards the mirror and face a picture or object in front of the mirror, and then compare it with its reflection by turning our head or body 180 degrees towards the mirror. It is thus not the mirror itself, but our own relative position and viewing point that has caused the apparent left-to-right reversal.

A mirror image appears three-dimensional if the observer moves. This is because the relative position of objects changes as the observer's perspective changes.[1]

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.


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