If any problem involving circular motion, which way does the acceleration vector point ?

the acceleration vector points towards the center of the circular path

Explanation: Acceleration is the rate of change of velocity ( is a vector quantity ) by the time interval in a motion. In uniform circular motion speed of moving object is constant but the direction of the velocity vector changes which causes an acceleration pointing to the center of the circle ( which is the path followed in circular motion ).

second mirror gathers light from a faraway object and reflects it to another mirror. - a.

see earlier answer