Microscope is Greek in both halves and modern in its assembly. Micro- is Greek mikros, "small," and -scope is from skopein, "to look at." But no Greek ever used the compound: the word is Modern Latin microscopium, coined in the 1650s for the newly invented instrument, meaning literally "an instrument for viewing what is small."
That is the standard shape of scientific vocabulary. When European scientists needed a name for something new, they built it from Greek parts rather than from their own languages, because Greek was the shared learned currency and its elements combined cleanly. Telescope, thermometer, barometer and photograph were all made the same way. The spelling tells you the parts are Greek; it does not tell you the word is old. La Caille even named a constellation Microscopium after the instrument in 1752.
microscope (n.) "optical instrument which by means of a lens or lenses magnifies and renders visible minute objects or details of visible bodies," 1650s, from Modern Latin microscopium , literally "an instrument for viewing what is small;" see micro- + -scope . The dim southern constellation Microscopium was among those introduced by La Caille in 1752. also from 1650s
microscope came in through Greek, and its spelling follows that family's conventions.
How that family writes these sounds
| a technical compound you could take apart | the combining forms: auto-, bio-, micro-, tele-, -logy, -graph, -meter, -scopebiography, microscope, telemetry |
What gives it away on the page
| auto-, bio-, micro-, tele-, -logy, -graph, -meter, -scope, -phobia | Combining forms, still productive today.biography, telemetry, microscope |