Editing Johannes Kepler (section)

=== ''Dioptrice'' ===
In the first months of 1610, [[Galileo Galilei]]—using his powerful new [[telescope]]—discovered four satellites orbiting Jupiter. Upon publishing his account as ''[[Sidereus Nuncius]]'' [Starry Messenger], Galileo sought the opinion of Kepler, in part to bolster the credibility of his observations. Kepler responded enthusiastically with a short published reply, ''Dissertatio cum Nuncio Sidereo'' [Conversation with the Starry Messenger]. He endorsed Galileo's observations and offered a range of speculations about the meaning and implications of Galileo's discoveries and telescopic methods, for astronomy and optics as well as cosmology and astrology. Later that year, Kepler published his own telescopic observations of the moons in ''Narratio de Jovis Satellitibus'', providing further support of Galileo. To Kepler's disappointment, however, Galileo never published his reactions (if any) to ''Astronomia Nova''.<ref>Caspar, ''Kepler'', pp. 192–197</ref>

Kepler also started a theoretical and experimental investigation of telescopic lenses using a telescope borrowed from Duke Ernest of Cologne.<ref>Koestler, ''The Sleepwalkers'' p. 384</ref> The resulting manuscript was completed in September 1610 and published as ''Dioptrice'' in 1611. In it, Kepler set out the theoretical basis of [[double-convex converging lens]]es and [[double-concave diverging lens]]es—and how they are combined to produce a [[Galilean telescope]]—as well as the concepts of [[real image|real]] vs. [[virtual image|virtual]] images, upright vs. inverted images, and the effects of focal length on magnification and reduction. He also described an improved telescope—now known as the ''astronomical'' or ''[[Keplerian telescope]]''—in which two convex lenses can produce higher magnification than Galileo's combination of convex and concave lenses.<ref>Caspar, ''Kepler'', pp.&nbsp;198–202</ref>