Telescope question?

Question

THe Keck telescopes in Hawaii have objective lenses 10 meters in diameter. If the diameter of your eye is 4mm, how many times more light is received by one of these telescopes than by your eye

Answer 1

Actually the diameter of the fully dark adapted human eye is about 7mm. Since telescopes are used to look at very dim objects, that is the figure to use. The light gathering power of the objective, lens or mirror, increases as the square of the diameter.
10m squared = 100m or 10,000cm.
7mm squared = 49mm or 4.9 cm
10,000cm / 4.9cm = 2041 X the light gathering power of the human eye.
Because of the way the human eye senses light, that means you will be able to see objects millions of times dimmer than with the naked eye.

Adolph

Answer 2

A 10 meter scope has an area equal to the square of the radius times Pi; or 5000mm x 5000mm x3.141 = 78,525,000 mm squared.

The Human eye has an area of 3.5mm x 3.5mm x 3.141 = 38.5 mm squared.

If the obstruction (secondary mirrors, supports, gaps, etc) in the 10M is about 15% (leaving a useful aperture of ~67,000,000mm sq), then objects in the scope will appear brighter by about 1.7 million times.

The biological component in this is not a constant, and the scope will be used with photography which adds the critical dimension of exposure time; but, the purpose of the tool is to capture and consentrate enough light to make extremely dim objects visible.

Answer 3

Well, they're not lenses, and I guess we're ignoring the fact that the mirror is not continuous over that diameter. It is in segments. But that should be a minor thing. (And as Cirric correctly said, there is the secondary mirror, which takes up some area.)

Take the area of the mirror, in mm. Pi times 5000^2. Now take the area of your pupil: pi times 2^2. Now divide that into the first number. Yeah, it's a BIG number.

Answer 4

Hi. Just figure the area of each, but be aware that the Keck scopes have an obstruction in the middle.