Special theory of relativity > The constancy of the light speed. Velocity addition > Problem 14.1.28

Statement

$14.1.28.$ The deflection angle of a proton with velocity $\beta c$ in a collision with another proton moving towards it at the same speed is $\alpha$. Determine the deflection angle of the first proton in a reference frame where the other proton is at rest before the collision.

Solution

Answer

$$\tan\alpha' = \sqrt{1-\beta^2}\tan \frac{\alpha}{2}.$$