# Can many small and far curved mirrors focus light just like as 1 big curved mirror?

Ok there was some dispute here (see comments) about the factibility of a sun-weapon, the dispute is that if mirrors are too small (compared to target's distance), they are subject to the pin-hole camera effect regardless the fact that the mirrors are convex or not.

So is there really a limit for that? Is this answer right even in the case the mirrors can be crafted with unlimited precision and the right amount of curvature?

• We can have a curved mirror that focus sun-light into a specific spot
• We cannot do that if use billions curved mirrors that are placed far away?

To recap: is that really impossible to burn anything on Earth by placing a huge amount of mirrors on the moon?

Why?

• Rather than focus (sorry) on the weapons aspect, what about considering roughly the same idea being used in adaptable optics telescopes en.wikipedia.org/wiki/Adaptive_optics – user108787 Aug 16 '16 at 12:42
• The folk who run the Keck Telescopes certainly hope so! – dmckee --- ex-moderator kitten Aug 16 '16 at 16:08
• You are only asking us to comment on other answers. What reasons do you have for siding with one view or the other? What is your own thinking about this problem? – sammy gerbil Aug 16 '16 at 19:23
• Nope I'm asking if there's really a limit on light focus done by a lens / mirror. My thinking on that is that if there's a limit, that's counterintuitive. The thermodynamics explaination is not convincing me (1 the mirror absorb partially some energy and 2 if you focus light in a point you remove light from elsewhere), so unless there's some other law I cannot see how that "weapon" could break energy conversation or heath dissipation – CoffeDeveloper Aug 17 '16 at 9:35

If you look up at a mirror in space reflecting the sun, it cannot be brighter than the sun. Therefore the energy reaching you is limited by the apparent size (angular size) of the mirror. The moon is about $0.5^{\circ}$ in angular diameter, the same as the sun, so if the whole moon was a mirror, we would experience two suns instead of one. This would be the case within a region with diameter about $3500~\mathrm{km}$ given by the half degree size of the sun. In order to make a weapon, one would need a larger mirror than this. A mirror orbiting the earth would be much smaller for the same angular size, and the region illuminated would also become correspondingly smaller.
If you take a lens, for example a photographic objective, with stop number f/1 and focus the sun on a piece of wood, the wood may take fire. But in this case the angular size of the lens opening as seen from the focal point is $60^{\circ}$.