[UPSC CSE 2006] Special Theory of Relativity (Q386, 25M)

The source S' moves along the x'-axis at a speed v, and emits light at an angle \theta' to the x'-axis of its own frame. In the S-frame the emitting angle with the x-axis is \theta. Here x and x'-axes are coincident. Show that the exact relativistic aberration formula \tan \theta = \frac{\sin \theta' \sqrt{1 - v^2 / c^2}}{\cos \theta' + v} can be derived from the velocity transformation relations.