# Comparing Light Collection Between Pupil and Telescope?

The amount of light collected for a period of time is proportional to the area of the collecting aperture. We use our eyes -pupils have diameters of approximately 5 mm-, binoculars and telescopes. How much more light can we collect with a 50mm pair of binoculars compared with our eyes? And with an 8-inch telescope? If we could have access to a 10-meter class professional telescope, how large would the gain be?

50^2/5^2= 100 times more light

8in = 203.2 mm

203.2^2/5^2= 1652 times more light

10000^2/5^2= 4000000 times more light

Did I solve this problem correctly?

• This is basically right in terms of total light from one small area of the sky that fits within the telescope's field of view. But remember when things (extended objects like nearby galaxies and nebulae) are magnified, the brightness is spread out to a larger area on the retina, so brightness per unit area has your aperture square term, but then divided by magnification squared.
– uhoh
Feb 1, 2018 at 14:49