Chapter 9, Problem 10CQ

(i) An object is placed at a position p > f from a concave mirror as shown in Figure CQ9.10a, where f is the focal length of the mirror. In such a situation, an image is formed at a distance q from the mirror, as we discuss in Chapter 26. The distances are related by the mirror equation:

$\frac{1}{p}+\frac{1}{q}=\frac{1}{f}$

In a finite time interval, the object is moved to the right to a position at the focal point F of the mirror. Show that the image of the object moves at a speed greater than the speed of light. (ii) A laser pointer is suspended in a horizontal plane and set into rapid rotation as shown in Figure CQ9.10b. Show that the spot of light it produces on a distant screen can move across the screen at a speed greater than the speed of light. (If you carry out this experiment, make sure the direct laser light cannot enter a person’s eyes.) (iii) Argue that the experiments in parts (i) and (ii) do not invalidate the principle that no material, no energy, and no information can move faster than light moves in a vacuum.

Figure CQ9.10