A plane mirror is initially kept vertical. A monochromatic light ray in the horizontal plane is incident on the mirror making an angle of 30∘ with the mirror surface.
(i) Calculate the initial angle between the incident and reflected rays.
(ii) The mirror is now rotated through 10∘ about a vertical axis so that its surface turns towards the incident ray. Without changing the direction of the incident ray, calculate the new angle of reflection.
(iii) Determine the total angle through which the reflected ray is deviated due to the rotation of the mirror.
(iv) Prove that, for any small rotation Δθ of a plane mirror about an axis perpendicular to its surface, the reflected ray turns through an angle 2Δθ.