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In theory, you could take a box, coat the inside with a mirroring material and have a smallish black object inside. Then cut a hole in one wall. Theoretically, a big part of the light entering the box would (after a few reflections) be absorbed by the object. If the abject is smaller than the hole, we a have a solar concentrator that works without tracking. Of course we loose power to the multiple reflections.

I wonder if anyone went to the trouble and optimised the shape of the box for this purpose.

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The more concentrated a solar collection system is, the narrower the angle over which it will accept useful energy. While the system that you describe sounds feasible, nobody who has designed systems of this sort has found it cost effective to use concentration ratios of more than about 2 to 3 to 1. Higher is possible but presumably the practical issues get too severe.

Examples of practical systems that do this are the many solar cookers with fold out mirrored or reflectorised flaps. These usually need to be moved a few times over the duration of a cooking session for optimum heating.

You'll find numerous real world examples here - each image links to a page.

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