The black circle with radius \(R_s\) represents the event horizon of the black hole.

Photons arrive from the right (\(x=+\infty\)

and \(y=b\)) with an impact parameter value \(b\)

that gives a deviation of \(4\pi\)

(2 full revolutions).

The figure is plotted with Cartesian coordinates \(x=r\cos\varphi\) and \(y=r\sin\varphi\),

considering a black hole of the mass

of the sun \(M\odot\)

that is \(R_s=2 \ 953\ m\), \(b_{crit}=7\ 672.73\ m\)

and with \(b_{4\pi} = 7\ 672.75\ m\).

The value of \(b\) is obtained by choosing the value of the final variation \(\Delta\varphi\) = deviation + \(\pi\)

(target value in Excel spreadsheet or input data in Python script).

Here, it is \(b_{crit} + 2\ cm\)

A deviation of \(8\pi\) (4 full revolutions) is obtained with \(b_{8\pi} = b_{crit} + 7\ 10^{-8}\ m\).

For a black hole with a different mass \(M\), the plots are kept by applying the scaling factor

\(\frac{M}{M\odot}\).