A laser beam is directed at a stationary plane mirror. The mirror is then slowly rotated about an axis in its plane while the direction of the incident beam remains fixed.
a. (a) The mirror is turned through 5∘. Prove that the reflected beam turns through 10∘.
b. (b) Before rotation, the incident beam made an angle of 35∘ with the normal. Calculate the new angle of reflection after the mirror has been rotated 5∘.
c. (c) Find the total angle between the original and the new reflected directions of the beam.