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I want to place a couple of mirrors outside the house to direct some sunlight to the windows, which will make it easier to cope with the soul-crushing overcast winters here in Melbourne, Australia.

In order to remain focused on a window, the position of the mirror would have to change to compensate for the change in the sun's position in the sky. One of the options is building a heliostat - a tracking system that employs a 2-axis control mechanism to rotate/shift the mirror. There are in fact commercial systems available to do exactly what I need - for example Sunflower Heliostat, that is $299.

I would like, however, to produce a more economic solution with no moving parts. One of the options is to build a long, concave mirror with a profile that takes into account the sun's position. Something like this:

enter image description here

On the surface it looks like a doable task, although I just wanted to check if I am missing something very obvious and my plan is doomed.

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Make sure the surface finish is akin to brushed aluminum. If it has a polish and anything falls in the focus, you will find you've underestimated how much solar energy you can capture with this. –  Fiasco Labs Apr 5 '13 at 1:34
    
All this is doing is increasing the square footage of mirror you are using to compensate for lack of motion. –  whatsisname Apr 5 '13 at 3:33
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The short answer is no.

You might be able to produce a curve that will reflect an arc (spanning the days extent from east to west) all day on a given day without moving it, but only a small portion of such a mirror will be going into your window at a given time, wasting the rest of its arc. Further, (as the season changes) your north-south alignment has to change, although this change is much slower.

A concave (focusing) mirror will have to be aimed to achieve concentration. Its focal length is a function of its curvature. You can simplify your control to 1 axis by using a polar mount.

Have a look at some of the Heliostat sites

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Thanks! I suspected that 2-axis shifting isn't there for nothing... –  Art Apr 5 '13 at 8:08
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