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You would want some sort of heliostat to track the source of illumination. After all, once the source moved, the angle of the incoming light to the initial reflective surface changes and the direction it is reflected to changes as well, resulting in the following series of mirrors not being hit by the incoming light. The first mirror would really be the only one needed to track the source of the illumination; all the others could remain static.
As to the effectiveness of it, mythbusters tested it.
EDIT: not sure if there is an actual term for this positioning, though I would refer to them as a series of mirrors or mirrors in a series ... possibly a daisy chain of mirrors ...