Galileo used a refractor i.e. no mirror: but what was the aperture?
Galileo's most famous invention was the telescope.
Galileo made his first telescope in 1609, modeled after telescopes produced in other parts of Europe that could magnify objects three times and its aperture was 1.5 cm.
He made/assembled two telescopes later in 1612/1620 that could finally magnify objects twenty times.
With this telescope, he was able to look at the moon, discover the four satellites of Jupiter, observe a supernova, verify the phases of Venus, and discover sunspots. His discoveries proved the Copernican system which states that the earth and other planets revolve around the sun. Prior to the Copernican system, it was held that the universe was geocentric, meaning the sun revolved around the earth.
Aperture Type Inventor (year)
Galileo's 1609 telescope  1.5 cm .62″ Refractor Galileo Galilei Italy (1609)
Galileo's 1612 telescope  2.6 cm 1″ Refractor Galileo Galilei Italy (1612)
Galileo's 1620 telescope  3.8 cm 1.5″ Refractor Galileo Galilei Italy (1620)