By what factor is the light-gathering power of the 10-m-diameter Keck telescope on Mauna Kea in Hawaii greater than an average unaided human eye,with a typical aperture diameter of 5 mm?
A) 2.5 × 10⁵ times
B) 2 × 10⁴ times
C) 2000 times
D) 4 × 10⁶ times

Question

Quizplus · Accepted Answer

The light-gathering power of a telescope is proportional to the square of its diameter.

The area of the Keck telescope is:
π(10m/2)² = 78.5 m²

The area of an average unaided human eye is:
π(0.005m/2)² = 1.96 x 10⁻⁵ m²

The ratio of their light-gathering power is:

(78.5 m²) / (1.96 x 10⁻⁵ m²) = 4.0 x 10⁶

Therefore, the light-gathering power of the Keck telescope is 4 x 10⁶ times greater than an average unaided human eye.

By What Factor Is the Light-Gathering Power of the 10-M-Diameter