A telescope with a 60 mm objective lens collects how many times as much light as does your eye's 6 mm pupil?

100 times

Explanation:

The light gathering power is the ability of a telescope to accumulate plenty of light than the human eye.

The area of the objective lens is given by:

Circular area = pi * diameter/4

Given diameter of telescope = 60mm

Diameter of human eye = 6mm

3.142*60^2/4) : (3.142*6^2/4)

Cancelling pi out leaves

(3600/4) : (36/4)

900/9 = 100 times

A telescope with a 60 mm objective lens collects approximately 100 times much light than 6 mm pupil of human eye.

Explanation:

The ability of a telescope to collect a lot more light than the human eye, is known as light gathering power.

To compare light-gathering powers of two telescopes or telescope and human eye, you divide the area of one telescope by the area of the other telescope.

Since the telescope is circular, we apply area of a circle.

(π*D²) / 4

Telescope : (π*60²) / 4 = 2827.8

Human eye (6 mm pupil) : (π*6²) / 4 = 28.278

Gathering power = 2827.8/28.278 = 99.97, approximately 100 times

Therefore, A telescope with a 60 mm objective lens collects approximately 100 times much light than 6 mm pupil of human eye.