A 2-m telescope can collect a given amount of light in 1 hour. Under the same observing conditions, how much time would be required for a 6-m telescope to perform the same task? A 12-m telescope?

Answer

given,

diameter of telescope = 2 m

time to collect area = 1 hour

Diameter of the another telescope = 6 m

The light collected by the telescope is directly proportional to the area of its primary mirror.

Area of the mirror is directly proportional to the square of diameter.

so,

6 m diameter telescope will carry (6/2) ² = 9 times more light than 2 m telescope.

Time taken to collect light = 60/9 = 6.67 minutes.

now, For 12 m telescope

12 m diameter telescope will carry (12/2) ² = 36 times more time than 2 m telescope.

Time taken by 12 m telescope to collect light = 60/36 = 1.7 minutes.