So for the problem, you have a flat mirror, a light source and a point A . The problem is to move the mirror in a way in wich the light source always hits the target point A, with the light source being able to move on an axis.
So this is basically the problem I've defined to simplify this situation: The light source and the point A are both above the mirror with constant heights $h_1$ and $h_2$. The mirror is fixed on a point and cannot move on the x or y axis, but it can rotate in relation to its center. The distance $k$ between the mirror and the point A in relation to the x axis is constant, and the the distance $x$ between the mirror and the light source in relation to the x axis is variable, since the light source can move in relation to the x axis. The problem is to find the inclination os the mirror as a function of the distance $x$. I don't really know how to proceed from now on to solve the problem.