A rotating platform carries a plane mirror whose reflecting surface is vertical. At t=0, a light ray is incident on the mirror at an angle of incidence of 30∘. The platform (and hence the mirror) begins to rotate about a vertical axis at a constant angular speed of 2∘s−1 in the clockwise sense as seen from above. The incident ray maintains its original direction throughout the motion.
(i) Derive an expression for the angular position of the reflected ray as a function of time t.
(ii) Calculate the angle between the initial and the final directions of the reflected ray after 4s of rotation.
(iii) At what instant will the reflected ray first become parallel to its initial direction of incidence?