Finding amount of light.

Question

A 1.22 m telescope can gather a given amount of light in 1.5 hour. Under the same viewing conditions, how much time would be required for a 4.26 m telescope to gather the same amount of light? Report your answer in minutes. Include the unit min for minutes in your answer and report your answer to one decimal place.

Answer 1

The times would be inversely related to the areas of the objectives lenses of the two telescopes:

 

pi·(1.22/2)²/pi·(4.26/2)² = t/1.5

1.22²/4.26² = t/1.5

 

Solve for t.  The units will be hours.  Multiply by 60 to convert to minutes.  The time will be smaller because the larger telescope has a larger light gathering area.