Chapter 2, Problem 66E

At $t=0$ , a bright beacon at the origin flashes, sending light uniformly in all directions. Anna is moving at speed v in the $+x$ direction relative to the beacon and passes through the origin at $t=0$ . (a) Show that according to Anna, the only light with a positive $x\text{'}$ −component is that which in the beacon’s reference frame is within an angle $\theta ={\cos }^{-1}(v/c)$ of the $+x$ −axis. (b) What are the limits of ? as v approaches 0 and as it approaches c? (c) The phenomenon is called the headlight effect. Why?