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:
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.