How much more light can the 5-m telescope at Mount Palomar collect from an astronomical source than can the unaided human eye (with a diameter of 5 mm)? A) 10⁶or 1,000,000 times B) 1000 times C) 10,000 times D) 5000 times

Question

Quizplus · Accepted Answer

The amount of light a telescope can collect compared to the human eye is proportional to the area of its aperture. The area of a circle (which is the shape of both the telescope's aperture and the pupil of the eye) is given by πr^2, where r is the radius of the circle. Since the diameter of the telescope is 5 m (or 5000 mm) and the diameter of the human eye is approximately 5 mm, the radius of the telescope's aperture is 2500 mm and the radius of the eye's pupil is 2.5 mm. Squaring these and taking the ratio gives (2500^2) / (2.5^2) = 1,000,000. Therefore, the 5-m telescope can collect 1,000,000 times more light than the unaided human eye.

How Much More Light Can the 5-M Telescope at Mount