Q: The pupil in your eye has a diameter of about 5 mm. The little telescope at the front of the class has a diameter of about 4.25 inches. What is the ratio of collecting area of the telescope to collecting area of the eye? Area of pupil: diameter(pupil) = 5 mm so radius(pupil) = (1/2) diameter = 2.5 mm 2 so area(pupil) = (pi) * (radius) 2 = (3.14) * (2.5 mm) = 19.6 square mm Area of scope: diameter(scope) = 4.25 inches = 108 mm so radius(scope) = (1/2) diameter = 54 mm 2 so area(scope) = (pi) * (radius) 2 = (3.14) * (54 mm) = 9161 square mm The ratio of these areas is area(scope) 9161 square mm ------------- = ---------------- = 467 area(eye) 19.6 square mm In other words, the telescope has 467 times the collecting are of the average human eye. How many times fainter are the faintest objects you can see in the telescope, compared to the faintest object you can see with your naked eye? The telescope collects 467 times as much light as the eye; therefore, one can see objects 467 times fainter with the telescope than with the eye alone.