A concave mirror focuses the rays of light exactly like a converging lens, and can thus be utilised as objective. In 1663, the Scottish mathematician James Gregory (1638-1675) (fig.1) proposed an instrument consisting of a main parabolic mirror, and an elliptical secondary one, which sent the optical beam back behind the primary mirror, which had a hole in it (fig.2). The Gregorian reflecting telescope (fig.3), which furnishes erect images (fig.4), met with great success in the 18th century thanks above all to the famous Scottish optician James Short (1710-1768) (fig.5).

In 1668, Isaac Newton (1642-1727) (fig.6) designed a telescope in which a plane mirror of elliptical shape, inclined by 45°, reflected the optical beam laterally, outside of the tube, where the eyepiece was positioned (fig.7). A second version (fig.8, fig.9), still existing today, was presented to the Royal Society in 1672.

In that same year the Frenchman Laurent Cassegrain (c. 1629-1693) proposed an instrument (fig.10) in which the secondary mirror, a convex hyperbolic one, was placed in front of the focus of the primary, focusing the image, as in Gregory's telescope, in back of the latter.

The first truly efficient reflecting telescope (fig.11) was a Newtonian one with a 6-inch aperture presented in 1721 to the Royal Society by the Englishman John Hadley (1682-1744) (fig.12). Its performance equalled that of Huygens' (1629-1695) refracting telescope 123 feet long. Although reflecting telescopes of large size were built during the 17th century (fig.13), the poor reflecting power of the mirrors of the time, made of a copper and tin alloy called speculum, that reflected only about 60% of the incident light, prevented the success of the reflecting telescope. The problem was solved in 1856, when Léon Foucault (1819-1868) (fig.14) and Karl August von Steinheil (1801-1870) (fig.15) invented the process of silver-plating that allowed the utilisation of mirrors made of glass covered with a very fine layer of the purest silver.