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reflection (n.)

late 14c., refleccioun, reflexioun, reflectioun, of surfaces or bodies, "the action of throwing back light or heat," from Old French reflexion, refleccion, and directly from Late Latin reflexionem (nominative reflexio) "a reflection," literally "a bending back," noun of action from past-participle stem of Latin reflectere "to bend back, bend backwards, turn away," from re- "back" (see re-) + flectere "to bend" (see flexible).

Meaning "an image produced by the action of a mirror, etc." is from 1580s. Of the mind, "turning of the thought back upon past experiences or ideas," from 1670s. Meaning "remark made after turning back one's thought on some subject" is from 1640s. Spelling with -ct- recorded from late 14c., established 18c., by influence of the verb. OED considers the version with -x- to be "the etymological spelling," but Fowler (1926) points out that -ct- is usual in the general senses and even technical ones.

A clear differentiation being out of the question, & the variation of form being without essential significance, the best thing to do is to use the commoner spelling, reflection, in all senses. [Fowler, "Modern English Usage," 1926]

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Definitions of reflection from WordNet

reflection (n.)
a calm, lengthy, intent consideration;
Synonyms: contemplation / reflexion / rumination / musing / thoughtfulness
reflection (n.)
the phenomenon of a propagating wave (light or sound) being thrown back from a surface;
Synonyms: reflexion
reflection (n.)
expression without words;
the pulse is a reflection of the heart's condition
Synonyms: expression / manifestation / reflexion
reflection (n.)
a likeness in which left and right are reversed;
Synonyms: mirror image / reflexion
reflection (n.)
the image of something as reflected by a mirror (or other reflective material);
he studied his reflection in the mirror
Synonyms: reflexion
reflection (n.)
(mathematics) a transformation in which the direction of one axis is reversed;
reflection (n.)
a remark expressing careful consideration;
Synonyms: observation / reflexion
reflection (n.)
the ability to reflect beams or rays;
Synonyms: reflexion / reflectivity
From wordnet.princeton.edu