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GeezerVison is showing mathworld.wolfram.com — Mirror Image -- from Wolfram MathWorld

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Mirror Image

MirrorSymmetry

A mirror image of a set S subset R^k is the image of S under reflection in an affine hyperplane. If the hyperplane is

H={x in R^k:(x-p)·n^^=0},

where n^^ is a normal vector of unit length, then the mirror image of a point x is

R_H(x)=x-2((x-p)·n^^)n^^.

The figure above illustrates the case p=0, with a point s and its mirror image s^' on opposite sides of the mirror plane W.

Reflection in a coordinate hyperplane reverses the sign of one coordinate and leaves the others unchanged. More generally, a reflection preserves all distances, so an object and its mirror image are congruent, but it changes handedness. A chiral object cannot be brought into coincidence with its mirror image using only translations and rotations. An object having mirror symmetry, by contrast, agrees with its mirror image for at least one mirror plane.

See also

Amphichiral, Chiral, Enantiomer, Handedness, Mirror Pair, Mirror Plane, Mirror Symmetry, Reflection, Symmetry

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References

Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., p. 87, 1967.

Referenced on Wolfram|Alpha

Mirror Image

Cite this as:

Weisstein, Eric W. "Mirror Image." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MirrorImage.html

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