How do reflection and refraction enable astronomers to build telescopes?

Answer 1

Light from a particular point of an object enters our eye nearly collimated (meaning as a shaft of nearly parallel beams of light). That column of light gets focussed by the lens in our eye to a point on our retina, which produces an image. The wider the column of light, the more light there is and the brighter that image will be. That is why our pupils dilate when it is dark, to see more light.

Our eyes however can only dilate so much. A telescope allows our eyes to take in a larger amount of light. It takes in a column of light from a particular object that is the size of the diameter of the scope's tube. The lens or mirror causes this light to converge into a point. Our eyes are not set up to view light in this way so there is then an eyepiece near the focal point of this converging light that then sort of undoes this and reformats the light back into a column, but a much smaller one that can fit within our pupil.

I made a diagram that shows how a newtonian reflector telescope works here: http://public.clunet.edu/~sjfahmie/optics2.gif

The red, green, and blue light columns are light from different point sources, lke stars. The colors mean nothing other than to differentiate the different sources of light.

Answer 2

Both can be used to focus light gathered from a wide aperture to a point small enough to pass through the pupil of the eye.

Lenses do it by bending the light, through the index of refraction of the lens material.

Reflection is used by a parabolic mirror to focus the reflected light to a point. This light is typically bent by a refractive lens before entering the eye.