A parabolic reflector -- all (specular) reflective, no "diffuse" or "transmissive" -- will get all the light from a point source going in the same direction. If you really want all the light doing that, you need an infinitely wide parabolic reflector so you'll get an infinitely wide beam. But if you're happy for, say, 99% of the light to end up in the beam, you can make a finite portion of a parabola that does that. Shrink it in towards the source and (aside from discretization issues) you will get as narrow a beam as you like with 99% of the light in it.
A real physical light source can never have zero size as the source here (aside from discretization issues) does. As a result, you can't get an arbitrarily narrow beam from it. There's a quantity called "etendue" that measures a sort of combination of spatial and angular spread-out-ness, and no combination of optical elements can decrease it except by absorbing some of the light.
A real physical light source can never have zero size as the source here (aside from discretization issues) does. As a result, you can't get an arbitrarily narrow beam from it. There's a quantity called "etendue" that measures a sort of combination of spatial and angular spread-out-ness, and no combination of optical elements can decrease it except by absorbing some of the light.