[hakonjdjohnsen]

> You make a big ring (roughly of the same area of the spot you are trying to make on the ground)

Unfortunately, this is not how the size of the spot on the ground is decided. Sunlight, even if reflected by a perfectly shaped mirror, spreads by approx 1 meter every hundred meters. At the "edge of space" at 100km, your spot already has a 1km diameter, in reality with a higher orbit and imperfect mirror & tracking it will be much larger. The size of your (ideal) mirror decides the brightness of the spot, not the size of the spot.

Liquid mirrors in space seem like a cool concept though!

[GistNoesis]

The area comment was more relative about the power received : To be able to have the power on the ground you need to reflect it from space (pointing the obvious that with 100sqm of surface area, you can't collect more power than surface area * power density). You also don't want to overheat everything (otherwise you need sun towers instead of solar panels), so a ball park of around 1:1 is a good starting point.

To focus light, the ideal shape is a parabola, and it's a shape that occur naturally when you spin liquid in gravity. (Their are process to build big telescopes which only point up). Of course you don't have gravity anymore, but you can pull on your surface with fields, or you can have concentric rings that you align more or less along the axis to deform the surface. We don't need perfect focus just a rough spot.