A laser sits at point L on an optical bench whose top is taken as the xy plane. Coordinates are in metres. The laser emits a narrow beam that travels in the +x direction and strikes a small, perfectly flat mirror located at the origin. The mirror can rotate only about the z axis (i.e., it can yaw but cannot pitch).
A light-sensitive detector is fixed at point D(0.50,0.50) on the bench. The height of the laser, mirror, and detector is identical, so the problem is two-dimensional.
The laser itself is at L(−0.60,0.20).
(a) Determine the angle that the incident beam makes with the normal to the mirror when the mirror’s reflecting surface is aligned along the y axis (i.e., normal along the x axis). Express your answer in degrees.
(b) The mirror is now rotated so that the reflected beam strikes the detector at D. Calculate the required angle, measured from the y axis to the mirror surface, that accomplishes this goal. Specify the direction of rotation (clockwise or counter-clockwise when viewed from above).
(c) Compute the new angle of incidence corresponding to the mirror orientation found in part (b) and verify explicitly that the path from L to the mirror and then to D satisfies the law of reflection.