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 variation of \(\Delta\varphi=\pi\) on entering
the event horizon.
The figure is plotted with Cartesian coordinates \(x=r\cos\varphi\) and \(y=r\sin\varphi\),
considering a hypothetical 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 \(b=6\ 582\ m\).
The value of \(b\) can be obtained by choosing a target value \(r=R_s\) for a variation \(\Delta\varphi\) of \(\pi\)
(Excel spreadsheet) or with the values \(R_s\) et \(\pi\) as input data (Python script).
This figure also corresponds to the emission of photons from the event horizon of the black hole (coordinates \(R_s\) and \(\pi\)) with an impact parameter \(b=6\ 582\ m\).
For a black hole with a different mass \(M\), the plots are kept by applying the scaling factor
\(\frac{M}{M\odot}\).