Question

How much more light gathering power does the 10 m telescope have than the human eye?

Option 1: 100 times

Option 2: 1,000 times

Option 3: 10,000 times

Option 4: 100,000 times

Answer 1

The 10 m telescope has 8,142,857 times more light-gathering power than the human eye.

Step-by-step explanation:

The light-gathering power of a telescope is determined by the size of its aperture, or mirror. The amount of light collected by a telescope is directly proportional to the area of its mirror. If we compare a 10 m diameter telescope to the human eye, which has a 7 mm (0.007 m) aperture, we need to calculate the ratio of their areas to determine the difference in light-gathering power.

The area of the 10 m diameter telescope is 314 m², while the area of the human eye is 0.0000385 m². Taking the ratio of these areas gives us:

314 m² / 0.0000385 m² = 8,142,857.14

Therefore, the 10 m telescope has 8,142,857 times more light-gathering power than the human eye. None of the options given (Option 1: 100 times, Option 2: 1,000 times, Option 3: 10,000 times, Option 4: 100,000 times) are correct.