Light gathering area,(LGA) is simply the area of the objective lens given by the formula for the area of a circle, A = pie* (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
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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.
LGP = (37/5)2 = 54.8.
Therefore Galileo's telescope gathered about 55 times more light that the eye.
Magnification can be defined as =is determined by dividing the focal length of the objective by the focal length of the eyepiece.
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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