Goldstein Central Force Repulsive Scattering

[decerto]

On page 108 in Goldstein 3rd edition in the paragraph after equation (3.94) he says that $\psi$` can be obtained from the orbit equation (3.36) using the limits as $r_0=\infty$ $r=r_m$ which the distance of closest approach and $\theta_0=\pi$ which is the initial direction.

So looking at the diagram on the top of the page this angle he is calculating $\theta$ seems to me to be exactly $\psi$ but he says that $\psi=\pi-\theta$

When we start at $r=\infty , \theta = \pi$ and move to $r=r_m$ on the diagram the corresponding angle traced out is $\theta=\psi$ where am I going wrong/The book is here for anyone who doesn't have it.

 

[Dale]

When we start at r=∞,θ=πr=\infty , \theta = \pi and move to r=rmr=r_m on the diagram the corresponding angle traced out is θ=ψ\theta=\psi where am I going wrong/

You start out at an angle of $\pi$ and trace out an angle $\psi$ so you must end up at an angle $\pi-\psi$.