Question

How much more light can be gathered by a telescope that is 8 m in diameter than by your fully dark-adapted eye at 7 mm?

Answer 1

1.32 million times more

Step-by-step explanation:

The amount of light gathered by the telescope and by the eye is proportional to their area, so we have to calculate the area of each and then compare them.

The telescope has a diameter of 8 m, so its radius is r = 4 m, and its area is

`A_t=\pi r^2 = \pi \cdot 4^2 = 50.3 m^2`

The eye has a diameter of 7 mm, so its radius is r = 3.5 mm = 0.0035 m, and its area is

`A_e = \pi r^2 = \pi \cdot (0.0035)^2=3.8\cdot 10^(-5) m^2`

So we can now compare the two areas:

`(A_t)/(A_e)=(50.3)/(3.8\cdot 10^(-5))=1.32\cdot 10^6`

So, the telescope can gather approximately 1.32 million times the light gathered by the eye.