sky-blue (adj.)

mid-13c. (c. 1200 as a surname), skie, sci, skei, "a cloud," from Old Norse sky "cloud," from Proto-Germanic *skeujam "cloud, cloud cover" (source also of Old English sceo (Middle English sceu) "the sky, the heavens," Old Saxon scio "cloud, region of the clouds, sky;" Old High German scuwo, Old English scua, Old Norse skuggi "shadow;" Gothic skuggwa "mirror"), from PIE root *(s)keu- "to cover, conceal."

The meaning "upper regions of the air; region of clouds, wind, and rain; the heavens, the firmament" is attested from c. 1300; it replaced native heofon in this sense (see heaven). In Middle English, the word can still mean both "cloud" and "heaven," as still in the skies (c. 1300), originally "the clouds."

Sky-high "as high as the sky" is from 1812; optimistic phrase the sky's the limit is attested from 1908. Sky-writing is from 1922. Sky-diving "sport or activity of jumping from an aircraft and free-falling before landing by parachute" is attested from 1959 (sky-diver by 1961; sky-dive (v.) by 1965).

"the color of the clear sky," c. 1300, from blue (adj.1). From late 15c. as "blue clothing." The blue is from 1640s as "the sky" (hence bolt from the blue "lightning," 1837); from 1821 as "the sea." In reference to a particular party which has chosen blue for its color, by 1835. "In most parts of England the Conservative party" [OED], but in 17c. it often was the Whig color (opposed to royal red).

Blue was by c. 1600 the distinctive color of the dress of servants, which may be the reason police uniforms are blue, a tradition Farmer dates to Elizabethan times. Blue as the color of police uniforms in U.S. is by 1853, when New York City professionalized its force. They previously had had no regular uniforms, only badges.

An outburst of indignation followed [the order to wear uniforms]. The men declared the order was a violation of their rights as free men ; that no respecting American would wear livery, and raised a fund of five hundred dollars to test in the courts the authority of the Commissioners to compel them to wear uniforms. But the order was enforced when the day came. [John Bach McMaster, "A History of the People of the United States,"  vol. viii, 1913] 

"sky-colored, sky-blue," 1660s, with -an + Latin caeruleus "blue, dark blue, blue-green," perhaps from a dissimilation of caelulum, diminutive of caelum "heaven, sky," which is of uncertain origin (see celestial). The Latin word was applied by Roman authors to the sky, the Mediterranean, and occasionally to leaves or fields. The older adjective in English was ceruleous (1570s). As a noun, from 1756. The artist's cerulean blue is from 1885.