Re: How can rainbows from a prism be made BIG with optics and still be bright

I didn't know the answer to this question right off the bat, so I asked
Professor David Gray, an astronomer at the University of Western Ontario.
He's an expert in the field of spectroscopy, the study of those "bands of
color" you mentioned in your question.

Regarding simultaneously big and bright spectra, he writes:

"You cannot do the impossible.  If the dispersion [size of the spectrum] is
increased...fewer photons will fall on a fixed-size pixel. That means not 
being able to observe as faint a star, or increasing the exposure time".

He refers to stars here,yet what he says is true, no matter where the light
is coming from.

The second part of your question was about separating the light. 
The answer is yes, you can certainly use filters to isolate a given color.
An ordinary mirror wouldn't work because mirrors reflect all wavelenghts
of visible light by definintion. 

If you want to collect all the light with wavelengths greater than a given
number, you can use a special type of filter called a dichroic.  This
differs from a regular filter because instead of letting a narrow set of
wavelengths shine through, a dichroic will pass a wide range of wavelenths.
Kind of like a low or high pass filter in electronics.

It is possible, but tricky to use a lens to isolate a given color of light.
I'd suggest just using a prism, or a grating to create your spectrum.