An astronomer wishes to construct a telescope that will brighten point sources by a factor of 16,900 times. If a human eye has an average has an average diameter of about 0.5 cm, what diameter should the telescope's primary lens/mirror be?
When an object is viewed through a telescope we are looking at the light emitted from it. As light travels the intensity decreases in an inverse square law relationship. An object that is twice is far away is going to appear 1/4 as bright as the light has spread over 4 times the distance. The path of light traveling from a point is in the shape of a cone.
The diameter of the human eye is 0.5 cm. If an object that is being viewed has to be brightened 16900 times, we need to collect light over an area that is 16900 times as large as the area of the human eye and focus it on to the area of the human eye.
This would require using a lens with diameter. `0.5*sqrt(16900)` = 0.5*130 = 65
If the light from an object is collected by a lens that has a diameter 65 cm and focused on the eye, it would ideally appear 16900 times as bright.