You can't light the spot with its own light? What does that even mean? With a mirror, I can reflect the beam of light from a laser pointer back to the origin. So what?
Therefore you can't light the earth warmer with it's own infrared radiation.
That infrared radiation comes from the Sun's energy. By reflecting back some of the radiation that's escaping the atmosphere, the Earth becomes warmer than if there were no such reflection. Are you going to argue that that's not the case? Seriously?
Nobody's claiming that the reflecting that radiation back makes the surface of the Earth hotter than the surface of the Sun, if that's what you're implying.
@cbae:I'm saying, just because you revert the beam back to it's origin, it's origin will not light up brighter.
The surrounding area will be brighter than if you don't reflect the beam back. Placing a torchiere floor lamp in the corner of a room lights up the entire room much brighter than if you put the lamp right in the center of a room.