Optical telescope
The telescope is more a discovery of optical craftsmen than an invention of a scientist. The lens and the properties of refracting and reflecting light had been known since antiquity and theory on how they worked were developed by ancient Greek philosophers, preserved and expanded on in the medieval Islamic world, and had reached a significantly advanced state by the time of the telescope's invention in early modern Europe. But the most significant step cited in the invention of the telescope was the development of lens manufacture for spectacles, first in Venice and Florence in the thirteenth century, and later in the spectacle making centers in both the Netherlands and Germany. It is in the Netherlands in 1608 where the first recorded optical telescopes (refracting telescopes) appeared. The invention is credited to the spectacle makers Hans Lippershey and Zacharias Janssen in Middelburg, and the instrument-maker and optician Jacob Metius of Alkmaar.
Lens (optics)
Spectacles were invented as an improvement of the "reading stones" of the high medieval period in Northern Italy in the second half of the 13th century. This was the start of the optical industry of grinding and polishing lenses for spectacles, first in Venice and Florence in the late 13th century, and later in the spectacle-making centres in both the Netherlands and Germany.
Spectacle makers created improved types of lenses for the correction of vision based more on empirical knowledge gained from observing the effects of the lenses (probably without the knowledge of the rudimentary optical theory of the day). The practical development and experimentation with lenses led to the invention of the compound optical microscope around 1595, and the refracting telescope in 1608, both of which appeared in the spectacle-making centres in the Netherlands.
With the invention of the telescope and microscope there was a great deal of experimentation with lens shapes in the 17th and early 18th centuries by those trying to correct chromatic errors seen in lenses. Opticians tried to construct lenses of varying forms of curvature, wrongly assuming errors arose from defects in the spherical figure of their surfaces. Optical theory on refraction and experimentation was showing no single-element lens could bring all colours to a focus. This led to the invention of the compound achromatic lens by Chester Moore Hall in England in 1733, an invention also claimed by fellow Englishman John Dollond in a 1758 patent.
Most lenses are "spherical lenses": their two surfaces are parts of the surfaces of spheres. Each surface can be "convex" (bulging outwards from the lens), "concave" (depressed into the lens), or "planar" (flat). The line joining the centres of the spheres making up the lens surfaces is called the "axis" of the lens. Typically the lens axis passes through the physical centre of the lens, because of the way they are manufactured. Lenses may be cut or ground after manufacturing to give them a different shape or size. The lens axis may then not pass through the physical centre of the lens.