There are a few reasons:
1. Not all wavelengths of light may pass through lenses. For example, infrared is easily absorbed by glass lenses, so we can't use them to take infrared pictures. Images of different wavelengths are useful for understanding temperature of stars or different objects in a galaxy etc. Mirrors reflect all wavelengths of light, which allows people to gather as much information as possible.
2. Lenses have more optical aberration problems, such as spherical and chromatic aberration. Don't be scared if you haven't seen the big words. They just mean that the lens can't focus all light to a single point, so the image will be unclear. Chromatic aberration results from different colors of light traveling with different speed in lenses. When a light beam passes through a lens, different colors will be refracted to different angles and won't be focused to one point. This is the reason why you can see different colors when sun light passes through a triangular prism. Spherical aberration comes from the fact that an ideal lens requires zero thickness, which is unattainable practically. People have come up with creative ways to reduce aberration, such as apochromatic lenses (http://en.wikipedia.org/wiki/Apochromat
), but they certainly increase the challenge of manufacture.
3. It is easier to make a large mirror than a large lens. A mirror only requires fabrication on one side; while a lens requires both. Moreover, to obtain high quality images, highly purified lenses are required, which increases the cost.
There are quite a few physics and engineering factors need to consider when building a powerful telescope. Using a large mirror (or an array of small mirrors) is indeed the major trend!
(published on 11/27/2011)