In 1609 Galileo Galilei heard of new invention by a Dutch optical maker that magnified distant objects. Within months Galileo had crafted his first telescope and turned it toward the sky. His observations were profound, shaking the very foundation of science and religion. By March of 1610 Galileo had written a discourse on his initial observations, which was published as Sidereus Nuncius (The Starry Messenger). Other publications soon followed with descriptions of mountains on the Moon, spots on the sun, bodies in orbit around Jupiter, the phases of Venus, and visions of stars where none appeared to the naked eye. Galileo, with this simple tool, transformed our understanding of the Universe.
Description of Galileo's telescope
By the end of the 13th century, craftsmen in Europe had developed magnifying glasses and had even mounted these lenses in frames to be worn on the face. In late 1608 Dutch spectacle makers mounted these lenses in combination and the telescope was invented. Galileo heard of this invention in 1609, and by the end of that year he had crafted several versions including the telescope that made the critical observations reported in Sidereus Nuncius. Galileo's original telescope had a 37mm diameter plano-convex objective lens with a focal length of 980mm. The original eyepiece was lost, but according to Galileo's writings was plano-concave with a diameter of about 22mm and a focal length of about 50 mm. These optical characteristics allow us to use a few simple formulas to calculate the powers of Galileo's telescope including the light gathering area, the light gathering power, the magnification of the telescope, and the focal ratio.
Light gathering area,(LGA) is simply the area of the objective lens given by the formula for the area of a circle, A = p (D/2) 2 , where D is the diameter (37 mm) and therefore D/2 is the radius (r) of objective (18.5 mm)
A = 3.14 x 18.52 = 1075 mm2 (10.75 cm2 or 1.7 in2)
Light gathering power (LGP) is defined as the ratio of the light gathering area of one instrument to another. Light gathering power is often compared to the human eye, the pupil of which has a diameter of about 5 mm. Therefore the LGA of Galileo's telescope can be compared to the LGA of the eye by the ratio
Canceling like terms in the numerator and denominator leaves us with
which is the square of the diameter of the telescope objective (Do) divided by the square of the diameter of the pupil of the eye (Dp) or LGP = (Do/Dp) 2 . For Galileo's telescope the answer is
LGP = (37/5)2 = 54.8.
Therefore Galileo's telescope gathered about 55 times more light that the eye.
Magnification (M) is determined by dividing the focal length of the objective by the focal length of the eyepiece. In the case of Galileo's telescope the focal length of objective was 980 mm and the focal length of eyepiece was -50 mm. We can ignore the minus sign as it just means that the eyepiece was a diverging lens. The magnification (M) is therefore determined by
Focal ratio (f/n), or f-number, is the ratio of the focal length of the objective to its diameter, and the smaller the f-number, the greater the amount of light per unit area reaches the image plane of the telescope. For Galileo's telescope with a focal length of 980 mm and an objective lens with a diameter of 37 mm the focal ratio is
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