| Light-gathering power is proportional to the area of the telescope
objective. A lens or mirror with a large area gathers a large amount of light.
Because the area of a circular lens or mirror of diameter D is pi(D/2)²,
we can compare the areas of two telescopes, and therefore their relative light-gathering
powers, by comparing the square of their diameters. That is, the ratio of the
light-gathering power (LGP) of the two telescopes A and B is equal to the ratio of their
diameters squared: LGPA / LGPB = (DA/DB)² Example A: Suppose we compare a 4cm telescope with a 24cm telescope. How much more light will the large telescope gather? Solution: LGP24 / LGP4 = (24/4)² = 6² =36 times more light Example B: Our eye acts like a telescope with a diameter of about 0.8cm, the
diameter of the pupil. How much more light can we gather if we use a 24cm telescope? LGP24 / LGPeye = (24/0.8)² = (30)² = 900 times more light. |