Light-gathering power

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

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?
Solution:

LGP24 / LGPeye = (24/0.8)² = (30)² = 900 times more light.

Back to Powers of a Telescope