ideayoudaoicibaDictYouDict
idea: [16] Etymologically, an idea is the ‘look’ of something – it comes ultimately from the same source as produced the Greek verb ídein ‘see’. Greek idéā itself was used by Plato in the specialized sense ‘archetypal form of something’, which survives in the derived adjective ideal [17], but as far as the modern English noun is concerned, its sense ‘notion, mental conception’ developed (in Greek) via ‘look, appearance’, ‘image’, and ‘mental image’. Ideology [18] is a derivative, coined originally in French at the end of the 18th century.
=> ideology, idol
idolyoudaoicibaDictYouDict
idol: [13] Greek eidos meant ‘form, shape’ (it came from the same root as idéā, source of English idea). From it was derived eídōlon, which originally meant ‘appearance’, and in particular ‘apparition, phantom’. It developed from there to ‘image’, either a ‘mental image’ or a ‘physical image’, such as a ‘statue’; and in the early Christian era it and its Latin descendant īdōlum were used for an ‘image of a false god’.

English acquired the word via Old French idole or idele. Another English offspring of Greek eidos, in the sense ‘picture’, is idyll [17], which was borrowed from the diminutive form eidúllion ‘little picture’, hence ‘small descriptive poem’.

=> idea, idyll
eidolon (n.)youdaoicibaDictYouDict
1801, "a shade, a specter," from Greek eidolon "appearance, reflection in water or a mirror," later "mental image, apparition, phantom," also "material image, statue, image of a god, idol," from eidos "form, shape" (see -oid). By 1881 in English as "a likeness, an image."
idol (n.)youdaoicibaDictYouDict
mid-13c., "image of a deity as an object of (pagan) worship," from Old French idole "idol, graven image, pagan god," from Late Latin idolum "image (mental or physical), form," used in Church Latin for "false god," from Greek eidolon "appearance, reflection in water or a mirror," later "mental image, apparition, phantom," also "material image, statue," from eidos "form" (see -oid). Figurative sense of "something idolized" is first recorded 1560s (in Middle English the figurative sense was "someone who is false or untrustworthy"). Meaning "a person so adored" is from 1590s.
imagine (v.)youdaoicibaDictYouDict
mid-14c., "to form a mental image of," from Old French imaginer "sculpt, carve, paint; decorate, embellish" (13c.), from Latin imaginari "to form a mental picture to oneself, imagine" (also, in Late Latin imaginare "to form an image of, represent"), from imago (see image). Sense of "suppose" is first recorded late 14c. Related: Imagined; imagining.