There's a great post relating to this on science blogs. Define the "radiance" of a source of illumination as the amount of light coming from it to the observer per unit of solid arc. In any passive optical system, the radiance is conserved. When you use a curved mirror, for instance, to focus the sun's rays on an observer, or a solid object to partly shade an obsever, what the observer sees is that the sun appears to take up more or less of the sky - the surface temperature of the sun appears the same.
The problem with the mirror setup is that you are proposing sources of light that are point sources - you are trying to divide by zero, to have a light source with infinite radiance. The moment you do this, all bets are off.
For any non-point source of light, the arrangement will not work. From the point of view of many of the points on the surface of the blue light source, the red light source will not occupy the whole of its field of view - the image of the red source in the larger ellipse is too small to completely obscure the image of the blue source behind it.