A laser beam is directed horizontally toward a narrow plane mirror mounted on a turntable at the center of a darkened laboratory. The incident beam, the mirror, and the reflected beam all lie in a horizontal plane. An angular scale attached to the turntable allows the experimenter to rotate the mirror by a measured small angle Δϕ about a vertical axis. The laboratory wall is 8.0 m away from the mirror and is marked with a protractor scale centered on the point where the incident beam would strike if the mirror were removed.
When the mirror is rotated, the bright spot produced by the reflected beam moves across the wall.
(a) Describe qualitatively the geometric relationship among the incident ray, the reflected ray, and the line perpendicular to the mirror surface (the normal).
(b) Explain, without numerical calculation, why the angular displacement of the reflected beam on the wall is expected to be twice the angular displacement Δϕ through which the mirror itself is rotated.
(c) The experimenter rotates the mirror by 2.0∘. Using the relationship you explained in part (b), predict the angular change of the reflected beam’s direction and calculate the lateral shift (in cm) of the bright spot on the wall 8.0 m away.