A coin is placed 12cm in front of a vertical plane mirror fixed on a wall. At the same instant, the mirror is pulled directly away from the coin with a uniform speed of 2cms−1 for 5s.
a. (i) State the initial distance between the coin and its image.
b. (ii) Calculate the distance between the coin and the mirror after 5s, and hence find the new position of the image.
c. (iii) Determine the total distance through which the image has moved during these 5s.
d. (iv) Show algebraically that, for any small displacement of a plane mirror along the normal, the displacement of the image is twice the displacement of the mirror.